Question

Write a quadratic equation given the solutions -4,-6

Answer 1

$x^{2} +6x+24$ is the quadratic equation with the solutions -4 and -6

Given that -4 and -6 are solutions of a quadratic equation and asked to find out the quadratic equation

If "a" and "b" are the roots of the quadratic equation then,

sum of roots = a+b

product of roots = ab

There the required quadratic equation is  $x^{2} -(a+b)x+ab$

Given that a= -4 and b= -6

sum of roots = a+b = -4 +(-6) = -10

product of roots = ab =( -4 )( -6 ) = 24

There the required quadratic equation is $x^{2} +10x+24$

Hence, $x^{2} +6x+24$ is the quadratic equation with the solutions -4 and -6

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