Question

If one zero of the polynomial 3 x square - 8 x + 2 k + 1 is 7 times the other find the value of k​

Answer 1

Given polynomial :

p(x) = 3x²-8x+(2k+1)

Here , it is given that one zero is seven times the second one.

So the second zero = α

First zero = 7α

We know the relationship between the constant term and the coefficient of x² .

Using this relationship we have :

$\alpha \times 7 \alpha = \frac{2k + 1}{3} \\ \\ 7 { \alpha }^{2} = \frac{2k + 1}{3} \\ \\ 21 { \alpha }^{2} = 2k + 1 \\ \\ 21 { \alpha }^{2} - 1 = 2k \\ \\ \frac{21 { \alpha }^{2} - 1}{2} = k$