Question

if the product of zeroes of the polynomial 4x2+3x+k is 4 find value of k​

Answer 1

★ Given :

• Polynomial : 4x² + 3x + k
• Product of zeroes of the polynomial is 4

★ To Find :

We have to find the value of k.

★ Explanation :

As, we have to find the value of k for which we are given the product of zeroes. So, if we will put value in the formula of product of zeroes we can calculate the value of k.

$\small{\star{\underline{\boxed{\sf{Product \: of \: zeroes = \dfrac{c}{a} }}}}}$

$\sf{\dashrightarrow 4 = \dfrac{k}{4}....(1)} \\ \\ \sf{\dashrightarrow k = 4 \times 4} \\ \\ \sf{\dashrightarrow k = 16} \\ \\ \large{\star{\underline{\boxed{\sf{k = 16}}}}}$

$\rule{400}{4}$

★ Verifaction :

For verification we will put value of k in equation (1).

We get,

$\sf{\dashrightarrow 4 = \dfrac{\cancel{16}}{\cancel{4}}} \\ \\ \sf{\dashrightarrow 4 = 4}$

$\mathbb{H} \bf{ence} \mathbb{V} \bf{erified}$

Answer 2

Given ,

The product of roots of polynomial is 4x² + 3x + k is 4

We know that , the product of roots i.e (αβ) is given by

$\star \sf \large \fbox{ \alpha \beta = \frac{c}{a} }$

Thus ,

$\sf \Rightarrow 4 = \frac{k}{4} \\ \\ \sf \Rightarrow k = 16$

$\therefore \sf \bold{ \underline{The \: value \: of \: k \: is \: 16 \: }}$