State whether the following statement is 'Tru | vedclass

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(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

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(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.

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