Question

For what value k will the sum of roots of equation x^2-x=k(5x-1)is zero.Please solve itfast , don't post any irrelevant answer​ Chapter POLYNOMIAL

Answer 1

$\large\underline{\sf{Solution-}}$

Given quadratic equation is

$\rm :\longmapsto\: {x}^{2} - x = k(5x - 1)$

can be rewritten as

$\rm :\longmapsto\: {x}^{2} - x = 5kx -k$

$\rm :\longmapsto\: {x}^{2} - x - 5kx + k = 0$

$\rm :\longmapsto\: {x}^{2} - x(1 + 5k) + k = 0$

We know that,

$\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

According to statement,

It is given that sum of the roots = 0

$\rm :\longmapsto\:\dfrac{5k + 1}{1} = 0$

$\rm :\longmapsto\:5k + 1 = 0$

$\rm :\longmapsto\:5k = - 1$

$\bf\implies \:k = - \: \dfrac{1}{5}$

Additional Information ;-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac