Question

if -2 and 3 are the zeros of the quadratic polynomial x2 + (a+1)x +b, the find a and b

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ value \ of \ a \ is \ -2 \ and \ b \ is \ -6.}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{x^{2}+(a+1)x+b}}$

$\sf{\implies{Zeroes \ are \ -2 \ and \ 3}}$

$\sf\pink{To \ find:}$

$\sf{The \ value \ of \ a \ and \ b.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{x^{2}+(a+1)x+b}}$

$\sf{Here, \ a=1, \ b=a+1 \ and \ c=b}$

$\sf{Sum \ of \ zeroes=\frac{-b}{a}}$

$\sf{\therefore{-2+3=\frac{-(a+1)}{1}}}$

$\sf{-a-1=1}$

$\sf{-a=1+1}$

$\sf{\implies{a=-2}}$

$\sf{Product \ of \ zeroes=\frac{c}{a}}$

$\sf{-2\times3=\frac{c}{a}}$

$\sf{-6=\frac{b}{1}}$

$\sf{\implies{b=-6}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ a \ is \ -2 \ and \ b \ is \ -6.}}}$

Answer 2

Answer:

Step-by-step explanation:

Thus, 2+(−3)=

1

−(a+1)

=>

1

(a+1)

=1

=>a+1=1

=>a=0

Also, 2×(−3) =

b=-6