We know that if
m and n are the roots of a quadratic equation ax²+bx+c=0, then the sum of the roots is (m+n) and the product of the roots is (mn). And then the quadratic equation becomes x²−(m+n)x+mn=0
Here, it is given that the roots of the quadratic equation are
m=3 and n=5, therefore,The sum of the roots is:
m+n=3+5=8
And the product of the roots is:
m×n=3×5=15
Therefore, the required quadratic equation is
= x²−(m+n)x+mn=0
⇒x²−8x+15=0
Hence, x²−8x+15=0
is the quadratic equation whose roots are 3and 5.
