Question

Find a quadratic polynomial each with the given numbers as the zeroes of the polynomial.

$3+\sqrt{7},3-\sqrt{7}$

• A. $x^2-x+2$
• B. $x^2-9x+2$
• C. $x^2-6x+2$
• D. $x^2-4x+2$

Answer 1

The correct option is C $x^2-6x+2$

Given roots: $3+\sqrt{7},3-\sqrt{7}$

Sum of the roots= $3+\sqrt{7}+3-\sqrt{7}$
= $6$

Product of the roots= $(3+\sqrt{7})(3-\sqrt{7})$
= $3^2-\left(\sqrt{7}\right)$
= $9-7$
= $2$

Now,the quadratic equation is given by,
$x^2-$(sum of roots)$x+$(product of the roots)
$=x^2-6x+2$