Class 10 Math All topics Polynomials

If one of the zeros of a quadratic polynomial of the form $x_{2}+ax+b$ is the negative of the other, then it

(a)

has no linear term and the constant term is negative

(b)

has no linear term and the constant term is positive

(c)

can have a linear term but the constant term is negative

(d)

can have a linear term but the constant term is positive

Correct answer: (a)

Solution: Given quadratic polynomial is,

$p(x)=x_{2}+ax+b$

Let one of the zero of the polynomial is $α$ then the other zero will be $−α$.

Sum of zeros=$α+(−α)=1−a $

=>$0=1−a $

=>$a=0$

and product of the zeros =$α(−α)=1b $

=>$−α_{2}=b$

=>$b=−α_{2}$

=>$b$ has to be negative.

Hence, option $A$ is correct.

We know that equation $ax_{2}+bx+c=0$

Then sum of roots $=a−b $ and product of roots$=ac $

$p(x)=x_{2}+ax+b$

Let one of the zero of the polynomial is $α$ then the other zero will be $−α$.

Sum of zeros=$α+(−α)=1−a $

=>$0=1−a $

=>$a=0$

and product of the zeros =$α(−α)=1b $

=>$−α_{2}=b$

=>$b=−α_{2}$

=>$b$ has to be negative.

Hence, option $A$ is correct.

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials