Question

If X=2/5 and X=-3 are roots of quadratic equation ax^2+7X+b=0 find value of a and b

Answer 1

Step-by-step explanation:

If X = 2/5 and X = -3

They both will satisfy following equation

If x= 2/5

a(2/5)^2 + 7(2/5)+b= 0

a (4/25) + 7×2/5 + b = 0

a (4/25) + 14/5 + b= 0

a (4/25 ) +b = -14/5

a+b = -14/5 × 25/4

a+b = -35/2...........(1)

If X= (-3)

a(-3)^2 + 7(-3) + b = 0

9a -21 +b = 0

a + b= 21/9

a + b = 7/3.......(2)

a = 7/3 -b....... (3)

Put (2) in (1)

a+b = -35/2

7/3 -b + b = -35/2

7 -3b/3 + b = -35/2

7 -2b = -35/2 ×3

7 + 35/2×1/3 = 2b

7 + 35/2 × 1/6 = b

b= 105/6 +7

b= 17.5 + 7

b= 24.5........(4)

Put (4) in (2)

a + b = 7/3

a = 7/3 - 24.5

a = 7-73.5/3

a = -66. 5/3

a = (-22.16)

So, a = (-22.16) and b = 24.5

Hope it helps you buddy