State whether the following statement is 'Tru | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The statement is False.Consider the general form of a quadratic equation: $ax^2 + bx + c = 0$.If the coefficient of $x$ is zero,then $b = 0$,and t

Vedclass · Accepted Answer

False

Vedclass · Answer

(B) The statement is False.Consider the general form of a quadratic equation: $ax^2 + bx + c = 0$.If the coefficient of $x$ is zero,then $b = 0$,and the equation becomes $ax^2 + c = 0$.The roots of this equation are given by $x^2 = -c/a$,which implies $x = \pm \sqrt{-c/a}$.For the roots to be real,we require $-c/a \geq 0$,which means $c/a \leq 0$.This occurs if $a$ and $c$ have opposite signs or if $c = 0$.For example,if $x^2 - 4 = 0$,then $x^2 = 4$,so $x = \pm 2$,which are real roots.Thus,the statement is false.

State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

Similar Questions

The value of the discriminant of the quadratic equation $5x^{2} + x + 2 = 0$ is ..... .

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} - 3x - 2 = 0$.

If the discriminant $D = 0$,then the roots of the quadratic equation $ax^2 + bx + c = 0$ are ..... .

Find the discriminant of the equation $3x^{2}-2x+\frac{1}{3}=0$ and hence find the nature of its roots. Find them,if they are real.

If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module