Question

If a+b =4 and a3+b3=44 then write a quadratic equation whose roots are a and b.

Answer 1

Concept:

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation.

Given:

An equation is given to us, $a^{3}+b^{3}=44$

To find:

The quadratic equation whose roots are a and b.

Solution:

An equation is given to us, $a^{3}+b^{3}=44$

Now, to find the roots of a and b, we will use the identity of $a^{3} +b^{3}=(a+b)^{3} -3ab(a+b)$

So, we will apply the identity in the given equation

$44=(4^{3})-3ab*4\\ 44-64=-12ab\\-20=-12ab\\ab=\frac{20}{12}\\ ab=\frac{5}{3}$

∴The quadratic equation is

$x^{2} +(a+b)x+ab=0\\x^{2} -4x+53=0\\3x^{2} -12x+5=0$

Hence, the answer is $3x^{2} -12x+5=0$

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