Question

If the roots of x²+Px+40=0 are in the ratio 2:5 , then find the value of P

Answer 1

Hey !!

◆ Quadratic Equations ◆

Check the attachment.
Hope it helps :)

Answer 2

Answer:

P =±14

Explanation:

Given:

If the roots of x²+Px+40=0 are in the ratio 2:5

To find :

Value of P

solution:

Let m, n are two roots of the

given quadratic equation.

m:n = 2:5

Let m = 2k,

n = 5k

Compare x²+Px+2=0 with ax²+bx+c=0, we get

a = 1 , b = P , c = 2

Now ,

i ) Sum of the roots = -b/a

=> 2k+5k = -P/1

=> 7k = -P

=> k = (-P/7)

=> k² = (-P/7)²

=> k² = P²/49 ----(1)

ii) Product of the roots = c/a

=> 2k×5k=40/1

=> 10k² = 40

=> 10×(P²/49) = 40 /* from (1)*/

=> P² = 40 × (49/10)

=> P² = 4×49

=> P = ±√(4×49)

=> P = ±√ (2×2)×(7×7)

=> P = ± (2×7)

=> P = ±14

Therefore,

P = ±14

••••