Question

4. Find a quadratic poly, whose zeros are 3,-7/5​

Answer 1

Hey, friend, here's your answer.

Let the zeroes be α and β.

In a quadratic polynomial, the general format is $ax^{2} + bx + c$.

Assuming the variable to be x, let us find out the coefficients!

$\alpha + \beta = \frac{-b}{a}$

$3 + \frac{-7}{5} = \frac{-b}{a} \\= \frac{15-7}{5} = \frac{8}{5}$

Hence, from this, we can see that,

- b = 8, b = -8

a = 5

Now we just need to find c,

$\alpha \beta = \frac{c}{a} \\= 3 \frac{-7}{5} = \frac{c}{a}$

Hence, c = -21

The final quadratic equation will be,

$5x^{2} - 8x -21$