Question

-5 is a root of quadratic equation 2x2 + px - 15 = 0 and quadratic equation P (X square + X) + K equal to zero has equal roots find the value of k​

Answer 1

$\textbf{Given:}$

$\text{-5 is a root of }2x^2+px-15=0$

$\implies\,2(-5)^2+p(-5)-15=0$

$\implies\,50-5p-15=0$

$\implies\,35-5p=0$

$\implies\,-5p=-35$

$\implies\boxed{\bf\,p=7}$

$\text{Also }\,7x^2+7x+k=0\;\text{has equal roots}$

$\implies\,b^2-4ac=0$

$\implies\,7^2-4(7)(k)=0$

$\implies\,49-28(k)=0$

$\implies\,-28k=-49$

$\implies\,4k=7$

$\implies\boxed{\bf\,k=\frac{7}{4}}$