Chapter 2 · Question 3

State the relationship between zeroes and coefficients of a quadratic polynomial.

Answer Revealed

Direct Answer:

For

p(x)=ax^2+bx+c

a\ne0

, if

\alpha

and

\beta

are zeroes, then

\alpha+\beta=-\frac ba

and

\alpha\beta=\frac ca

For a quadratic, sum of zeroes is negative coefficient of

x

over coefficient of

x^2

; product is constant term over coefficient of

x^2

Let

p(x)=ax^2+bx+c

and zeroes be

\alpha,\beta

. Then

p(x)=a(x-\alpha)(x-\beta)=a[x^2-(\alpha+\beta)x+\alpha\beta]

. Comparing coefficients with

ax^2+bx+c

gives

-a(\alpha+\beta)=b

and

a\alpha\beta=c

. Hence

\alpha+\beta=-\frac ba

and

\alpha\beta=\frac ca

For $p(x)=ax^2+bx+c$ , $a\ne0$ , if $\alpha$ and $\beta$ are zeroes, then $\alpha+\beta=-\frac ba$ and $\alpha\beta=\frac ca$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

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