Find the quadratic equation, whose roots are $5$ and $-4$ and leading coefficient is $3$ ?

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Answer 1 · 2017-04-01T16:26:55

$3x^2-3x-60=0$

A quadratic equation whose roots are $alpha$ and $beta$ and leading coefficient is $a$ is

$a(x-alpha)(x-beta)=0$

Hence, the quadratic equation whose roots are $5$ and $-4$ and leading coefficient is $3$ is

$3(x-5)(x-(-4))=0$

or $3(x-5)(x+4)=0$

or $3(x^2-5x+4x-20)=0$

or $3(x^2-x-20)=0$

or $3x^2-3x-60=0$

Find the quadratic equation, whose roots are 55 and -4-4 and leading coefficient is 33?