Question

30x^2-ax-a^2=0 find the roots of the quadratic equation by factorisation​

Answer 1

ANSWER:

Given:

• 30x² - ax - a² = 0

To Find:

• Roots of the equation

Solution:

We are given that,

$\implies 30x^2-ax-a^2=0$

Here we can see that,

• The product of roots should be -30a²x²
• The sum of the roots should be -ax

So, the middle term will be split into 5ax and -6ax.

Hence,

$\implies 30x^2-ax-a^2=0$

$\implies 30x^2+5ax-6ax-a^2=0$

Taking 5x common,

$\implies 5x(6x+a)-6ax-a^2=0$

Taking -a common,

$\implies 5x(6x+a)-a(6x+a)=0$

Now, we will take (6x + a) common,

$\implies (6x+a)(5x-a)=0$

So,

$\implies 6x+a=0\:\:\&\:\:5x-a=0$

$\implies 6x=-a\:\:\&\:\:5x=a$

Hence,

$\implies x=\dfrac{-a}{6}\:\:\&\:\:x=\dfrac{a}{5}$

Therefore,

$\implies\bf x=\dfrac{-a}{6}\,,\:\dfrac{a}{5}$