If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ________ roots.

Open in App

Solution

Let $a x^{2} + 0 x + c = 0$ be a quadratic equation.

It is given that, coefficient of x² and the constant term of a quadratic equation have the same sign
⇒ ac > 0
⇒ 4ac > 0
⇒ −4ac < 0
⇒ 0²−4ac < 0
⇒ Discriminant < 0
⇒ Roots are imaginary

Hence, if the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has imaginary roots.

Suggest Corrections

Similar questions

If the coefficient of

x^{2}

and the constant term have the same sign and if the coefficient of

x

term is zero, then the quadratic equation has :

Question 2 (vi)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Q. If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the roots of the quadratic equation are
______ and _______.

Question 2 (v)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Join BYJU'S Learning Program

If the coefficient of x2 and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ________ roots.

If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ________ roots.