Question

Write the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4.

Answer 1

The quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4 is $4 x^{2}-36 x+80=0$

Solution:

Given that, roots of an quadratic equation are 4 and 5.

We have to find the equation of the quadratic equation.

Now, as 4 and 5 are roots, x = 4 and x = 5

Which means x – 4 and x – 5 are factors of the quadratic equation.

Then, equation will be the products of the factors

So, equation is (x - 4)(x - 5) = 0

Upon multiplication we get,

$\begin{array}{l}{x(x-5)-4(x-5)=0} \\\\ {x^{2}-5 x-4 x+20=0} \\\\ {x^{2}-9 x+20=0}\end{array}$

As we are given that, leading coefficient of the equation is 4. So multiply equation with 4

$\begin{array}{l}{\rightarrow 4\left(x^{2}-9 x+20=0\right)} \\\\ {\rightarrow 4 x^{2}-36 x+80=0}\end{array}$

Hence, the quadratic equation is $4 x^{2}-36 x+80=0$