Algebra Ex 3.9-10th Std Maths-Book Back Question And Answer
Question 1.
Determine the quadratic equations, whose sum and product of roots are
(i) -9, 20
Answer:
Sum of the roots = -9 and Product of the roots = 20
The Quadratic equation is
x2 – (sum of the roots) x + product of the roots = 0
x2 – (-9) x + 20 = 0 ⇒ x2 + 9x + 20 = 0
(ii) 53, 4
Answer:
Sum of the roots = 53; Product of the roots = 4
The Quadratic equation is
x2 – (sum of the roots) x + product of the roots = 0
x2 – (53) x + 4 = 0 ⇒ x2 – 53 x + 4 = 0
3x2 – 5x + 12 = 0
(iii) −32, -1
Answer:
Sum of the roots = −32; Product of the roots = -1
The Quadratic equation is
x2 – (sum of the roots) x + product of the roots = 0
x2 – (-32) x + (-1) = 0 ⇒ x2 + 32 x – 1 = 0
2x2 + 3x – 2 = 0
(iv) – (2 – a)2, (a + 5)2
Answer:
Sum of the roots = – (2 – a)2; Product of the roots = (a + 5)2
x2 – (sum of the roots) x + product of the roots = 0
x2 – [-(2 – a)2] x + (a + 5)2 = 0
x2 + (2 – a)2 x + (a + 5)2 = 0
Question 2.
Find the sum and product of the roots for each of the following quadratic equations
(i) x2 + 3x – 28 = 0
(ii) x2 + 3x = 0
(iii) 3 + 1a=10a2
(iv) 3y2 – y – 4 = 0
Solution:
(i) x2 – (-3)x + (-28) = 0.
Comparing this with x2 – (α + β)x + αβ = 0.
(α + β) = Sum of the roots = -3
αβ = product of the roots = -28
(ii) x2 + 3x = 0 = x2 – (-3)x + 0 = 0
x2 – (α + β)x + αβ = 0
Sum of the roots α + β = -3
Products of the roots αβ =0
(iii) 3 + 1a = 10a2
Answer:
Multiply by a2
3a2 + a = 10
3a2 + a – 10 = 0
Sum of the roots (α + β) = −13
Product of the roots (α β) = −103
(iv) 3y2 – y – 4 = 0
Answer:
Sum of the roots (α + β) = −(−1)3 = 13
Product of the roots (α β) = −43
