Question

Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let, $f\left(x\right)=3x^2-75=0$

$\Rightarrow 3x^2-75=0$

$\Rightarrow x^2-25=0$

$\Rightarrow (x-5)(x+5)=0$

$\Rightarrow x=-5,5$

So, zeros of quadratic equation are $5and-5$

Verification:

Sum of zeros $=\frac{-coeficientofx}{coeficientof{x}^2}$

$\Rightarrow 0=\frac{-0}{3}$

$\Rightarrow 0=0$

And,

Product of zero $=\frac{constantterm}{coeficientof{x}^2}$

$\Rightarrow 5\times -5=\frac{-75}{3}$

$\Rightarrow -25=-25$

Hence, verified.