Question

If -4 is a root of the equation x2+px-4=0 and equation 2x2+px+k=0 has equal roots find k and p

Answer 1

Answer:

k = -20

Explanation:

i) It is given that -4 is a root

of the quadratic equation

x²+px-4=0,

=> (-4)²+p(-4)-4 = 0

=> 16-4p-4 = 0

=> 12-4p = 0

Divide each term by 4 , we get

=> 3-p = 0

=> p = 3 ------(1)

ii ) -4 is a root of one root

of 2x²+px+k = 0

=> 2(-4)²+p(-4)+k = 0

=> 32-4p+k = 0

put p=3 , we get

=> 32-4×3 +k = 0

=> 32 -12 + k = 0

=> 20 + k = 0

=> k = -20

Therefore,

k = -20

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