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  • If -5 is a root of the quadratic equation 2x² + px - 15 = 0 and the quadratic equation P(x² + x) + k=0 has equal roots , find the value of k.

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

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best_answer

If -5 is a root of the quadratic equation 2 x^{2}+p x-15=0

So 2(-5)^{2}+p(-5)-15=0

So p=7

So the equation p\left(x^{2}+x\right)+k=0 

becomes 7\left(x^{2}+x\right)+k=0

or 7 x^{2}+7 x+k=0

And equation 7 x^{2}+7 x+k=0 has equal roots

So D ( Discriminant ) $=b^{2}-4 a c$=0

i.e b^{2}-4 a c$=7^2-(4*k*7)=0

So we get

k=\frac{7}{4}

Posted by

avinash.dongre

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