If the zeroes of the quadratic polynomial ax^ | vedclass

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

Question

(C) For a quadratic polynomial $ax^{2} + bx + c$,the zeroes are equal if the discriminant $D = b^{2} - 4ac = 0$.This implies $b^{2} = 4ac$.Since $b^{2

Vedclass · Accepted Answer

$c$ and $a$ have the same sign

Vedclass · Answer

(C) For a quadratic polynomial $ax^{2} + bx + c$,the zeroes are equal if the discriminant $D = b^{2} - 4ac = 0$.This implies $b^{2} = 4ac$.Since $b^{2}$ is always non-negative for any real $b$,$4ac$ must be non-negative.Given $c 
eq 0$,if $a = 0$,it would not be a quadratic polynomial. Thus,$a 
eq 0$.Since $4ac = b^{2} \geq 0$,the product $ac$ must be greater than or equal to $0$.Since $c 
eq 0$ and $a 
eq 0$,$ac > 0$,which means $a$ and $c$ must have the same sign.For example:$(i)$ $x^{2} + 4x + 4 = 0 \Rightarrow (x+2)^{2} = 0 \Rightarrow x = -2, -2$ (Here $a=1, c=4$,both positive).$(ii)$ $x^{2} - 4x + 4 = 0 \Rightarrow (x-2)^{2} = 0 \Rightarrow x = 2, 2$ (Here $a=1, c=4$,both positive).

If the zeroes of the quadratic polynomial $ax^{2} + bx + c, c \neq 0$ are equal,then

Similar Questions

The graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis $\ldots \ldots \ldots \ldots$

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 3x^{2} - 6x + 8$,then $\alpha \beta \gamma = \dots$

The zero of the linear polynomial $p(x) = ax + b$ is $\ldots \ldots \ldots \ldots$ $(a, b \neq 0)$.

The coefficient of the underlined term of $p(x) = 7 - \underline{5x^4} - 2x^3 - x^2$ is $\ldots \ldots$

The sum of the zeros of a quadratic polynomial $p(x) = 3x^2 + 7x + 4$ is...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module