Question

 If one of the roots of the polynomial 16x²+kx+21 is 7/3 times the other then what is the value of k​

Answer 1

Step-by-step explanation:

Let one root be x

Then

Other root will be

$\\ \sf\hookrightarrow \dfrac{7}{3}x$

$\\ \sf\hookrightarrow \dfrac{7x}{3}$

We know that

$\boxed{\sf Sum\:of\:roots=\dfrac{-b}{a}}$

$\\ \sf\hookrightarrow x+\dfrac{7x}{3}=\dfrac{-k}{16}$

$\\ \sf\hookrightarrow \dfrac{3x+7x}{3}=\dfrac{-k}{16}$

$\\ \sf\hookrightarrow \dfrac{10x}{3}=\dfrac{-k}{16}$

$\\ \sf\hookrightarrow 10x(16)=-3k$

$\\ \sf\hookrightarrow 160x=-3k$

$\\ \sf\hookrightarrow k=\dfrac{160}{-3}$

$\\ \sf\hookrightarrow k=53.3$

$\\ \sf\hookrightarrow k=53(Approx)$