Question

1. Form a quadratic equation if its roots are 1/2 and-3/5​

Answer 1

In a quadritic equation, we know that

-b/a = α + β (here, α and β are two roots)

and, c/a = αβ

So, if the coefficient a = 1.

Then, -b = α + β. (here, a=1)

= 1/2 + (-3/5)

= -1/10

b = 1/10; (i)

and, c = αβ. (if, a=1)

= 1/2 × (-3/5)

= -3/10; (ii)

Now, the general form of a quadritic equation is;

ax^2 - bx + c = 0

Now, we have taken, a=1;

Thus, x^2 - bx + c = 0

From equation (i) and (ii);

= x^2 - (1/10)x + (-3/10) = 0

= x^2 - x/10 - 3/10 = 0

= 10x^2 - x - 3 = 0

Thus the required quadritic equation is 10x^2 - x - 3.

That's all.