WBBSE Solutions For Class 10 Maths Chapter 1 Quadratic Equations In One Variable Exercise 1.5

Chapter 1 Quadratic Equations In One Variable Exercise 1.5

Wbbse 10th Maths Exercise 1.5 Question 1.

Let us write the nature of two roots of the following quadratic equations:

1. 2x² + 7x+3=0

2. 3x²-2√6x+2=0

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3. 2x²– 7x+9=0

4. 2/5 x²-2/3x+1=0

Wbbse 10th Maths Exercise 1.5  Question 2.

By calculating, let us write the value/values of k for which each of the following quadratic equations has real and equal roots-

1. 49x² + kx + 1 = 0

2. 3x²-5x+2k = 0

 

3. 9x²-24x + k = 0

4. 2x² + 3x + k=0

5. x²-2 (5+ 2k) x + 3 (7+10k) = 0

6. (3k+ 1)x² + 2 (k+1)x + k = 0

Wbbse 10th Maths Exercise 1.5  Question 3.

Let us form the quadratic equations from two roots given below-

1. 4, 2

Solution: When roots are 4, 2:1

The required equation: x² (Sum of the roots) x + product of roots = 0 i.e., x² – (4+2)x + 4.2 = 0

or, x²-6x+8=0

2.-4, -3

Solution: When roots are -4, -3:

The required equation:- x² – (Sum of the roots) x + product of the roots = 0

i.e. ; x²(43) x + (-4) (-3)=0

or, x² + 7x+12=0

3. -4, 3

Solution: When roots are -4, 3:

The required equation: x² – (Sum of the roots) x + product of the roots = 0

i.e., x²-(-4+3) x + (-4).3 = 0

or, x² + 1x-12=0

or, x²+x-12=0

4. 5, -3

Solution: When roots are 5, -3:

The required equation: x² – (Sum of the roots) x + product of the roots = 0

i.e., x² (5-3) x + 5 (-3)=0

or, x²-2x-15=0+

Wbbse Quadratic Equation With One Variable Question 4.

For what value of m the two roots of the quadratic equation 4x² + 4 (3m -1) x + (m +7)=0 are reciprocal to each other?

Wbbse 10th Maths Exercise 1.5  Question 5.

If two roots of the quadratic equation (b-c)x² + (ca)x + (a – b) = 0 are equal, then let us prove that, 2b = a + c.

Question 6. If two roots of the quadratic equation (a²+ b²)x² -2 (ac + bd)x + (c² + d²) = 0 are equal, then let us prove that, a/c = b/d

Wbbse Quadratic Equation With One Variable Question 7.

Let us prove that the quadratic equation 2(a² + b²)x² + 2 (a + b) x + 1 = 0 has no real root if a b.

Wbbse Quadratic Equation With One Variable Question 8.

If two roots of the quadratic equation 5x²+2x-3= 0 are x and ẞ, then let us determine the value of :

1. α²+ β²

(2) α³ +ẞ³

(3) α² /B + B²/ α

Wbbse Quadratic Equation With One Variable Question 9.

If one root of the equation ax² + bx + c = 0 is twice of the other, then let us show that 2b² = 9ac.

Question 10. Let us form the equation whose roots are reciprocals to the roots of equation x² + px + 1 = 0.

Wbbse Class 10 Maths Exercise 1.5 Solutions Question 11.

Let us determine the equation whose roots are a square of the roots of equation x² + x + 1 = 0.

Chapter 1 Quadratic Equations In One Variable Exercise 1.5 Multiple Choice Questions

Wbbse Class 10 Maths Exercise 1.5 Solutions Question 1.

The sum of the two roots of the equation x²-6x + 2 = 0 is

1. 2

2. -2

3. 6

4. -6

Solution: Sum of the roots = – (-6)/1= 6………………(c)

 

Question 2. If the product of two roots of the equation x² – 3x + k = 10 is -2, then the value of k is

1. -2

2. -8

3. 8

4 12

Solution: or, x² – 3x + (k-10) = 0

Product of the roots = k -’10

K-10=-2              k10-28 —–(c)

 

Wbbse Class 10 Maths Exercise 1.5 Solutions

Question 3. If two roots of the equation ax² + bx + c = 0 (a + 0) are real and unequal, then b² -4ac will be

1. > 0

2. = 0

3. < 0

4. None of these

Solution: The roots of the equation ax² + bx + c = 0 (a + 0)

are real & unequal if b²-4ac >0—– (a).

Product of the roots = k -’10

k-10=-2              k10-28 —–(c)

Wbbse Class 10 Maths Exercise 1.5 Solutions

Question 4. If two roots of the equation ax2 + bx + c = 0 (a + 0) are real and unequal, then b2 -4ac will be

1. > 0

2. = 0

3. < 0

4. None of these

Solution: The roots of the equation ax2 + bx + c = 0 (a + 0)

are real & unequal if b²-4ac >0—– (a).

Question 5. If two roots of the equation ax2 + bx + c = 0 (a + 0) be equal, then

1. c=-b/2a

2. c=b/2a

3. c= -b²/4a

4. c=b²/4a

Solution: The roots of the equation ax2 + bx + c = 0 will be equal if b2 = 4ac.

or, c =b²/4a

 

Question 6. If two roots of the equation 3x² + 8x+2=0 be∞ and ẞ, then the value of (1/∞+1/ ẞ) is

1. -3/8

2. 2/3

3. -4

4. 4

 

Wbbse Class 10 Maths Exercise 1.5 Solutions

Chapter 1 Quadratic Equations In One Variable Exercise 1.5 True or False:

Question 1. The roots of equation x² + x + 1 = 0 are real.

Answer: False, as here b²-4ac1-4.1.1-4 <1.

Question 2. The roots of the equation x² – x + 2 are not real.

Answer: True, as here b²-4ac = (-1)2-4.1.2-1-8-7 <1.

Chapter 1 Quadratic Equations In One Variable Exercise 1.5  Fill in the blanks:

Question 1. The ratio of the sum and the product of two roots of equation 7x² – 12x + 18 = 0 ——————-

Question 2. If two roots of the equation ax² + bx + c = 0 (a + 0) are reciprocal to each other, then c =—————–

Question 3. If two roots of the equation ax² + bx + c = 0 (a + 0) are reciprocal to each other and opposite (negative),

Chapter 1 Quadratic Equations In One Variable Exercise 1.5 Short Answers

1. Let us write the quadratic equation if the sum of its roots is 14 and the product of them is 24.

Solution: The sum of the roots. 14 & the product of the roots = 24.

The required equation is x² – 14x + 24 = 0.

2. If the sum and the product of two roots of the equation kx² + 2x + 3k = 0 (k = 0) áre equal, let us write the value of k.

3. If x and ẞ be the two roots of the equation x² – 22x + 105= 0, let us write the value of (x – B)

4. If the sum of two roots of the equation x²-x= k (2x-1) is zero, let us write the value of k.

5. If one of the roots of the two equations x² + bx+12= 0 and x² + bx + q = 0 is 2, let us write the value of q.