For a quadratic equation $a x^{2} + b x + c = 0$ , if sum of the roots is - 1 and product of the roots is 1, then which of the following holds true?

a^{2} = b c

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a c = 1

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a b = 1

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b c = 1

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Solution

The correct option is A $a^{2} = b c$
Quadratic equation $a x^{2} + b x + c = 0$
Sum of roots, $- \frac{b}{a} = - 1 \Rightarrow b = a$
Product of roots $\frac{c}{a} = 1 \Rightarrow c = a$
On comparing,
we get
$a^{2} = b c$

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For a quadratic equation ax2+bx+c=0, if sum of the roots is - 1 and product of the roots is 1, then which of the following holds true?

The correct option is A a2=bcQuadratic equation ax2+bx+c=0 Sum of roots, −ba=−1⇒b=a Product of roots ca=1⇒c=a On comparing, we get a2=bc

For a quadratic equation $a x^{2} + b x + c = 0$ , if sum of the roots is - 1 and product of the roots is 1, then which of the following holds true?

The correct option is A $a^{2} = b c$
Quadratic equation $a x^{2} + b x + c = 0$
Sum of roots, $- \frac{b}{a} = - 1 \Rightarrow b = a$
Product of roots $\frac{c}{a} = 1 \Rightarrow c = a$
On comparing,
we get
$a^{2} = b c$