Question

if -5 is a root of the quadratic equation 2x2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots. find the value of k

Answer 1

k= 7/4

Explanation:

2x²+px-15=0

One of roots is -5, then:

• 2*(-5)²- 5p -15 =0
• 50 -5p - 15= 0
• 5p= 35
• p=7

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p(x²+x)+k=0

replacing value of p:

• 7(x²+x)+k=0
• 7x²+7x+k=0

it has equal roots, then the discriminant is zero:

b² - 4ac=0

• 7²-4*7*k=0
• 7 -4k=0
• 4k=7
• k= 7/4