Question

If one zero of the polynomial x² -3x-10 is -2 then another zero will be .........​

Answer 1

$\sf\huge\red{\underbrace{ Solution : }}$

$\rm\blue{\underline{\mapsto \: Given\:that :}}$

• Polynomial p(x) = x² - 3x - 10
• One of the zero of the polynomial of p(x) is - 2.

$\rm\orange{\underline{ \mapsto To\:find :}}$

• Another zero of the polynomial p(x).

$\rm\green{\underline{ \mapsto Let :}}$

➡ According to the Quadratic Polynomial : “ ax² + bx + c = 0 ” , consider the polynomial p(x) as

1. a = 1
2. b = - 3
3. c = - 10

➡ And the zero of the polynomial be

• α = - 2

$\rm{\red{\underline{ \mapsto Now:}}}$

$\boxed{\bf{\purple{ \rightarrow Sum\:of\:the\:zeroes : \alpha+\beta=-\cfrac{-b}{a} }}}$

$\sf \implies - 2 +\beta = -\cfrac{(-3)}{1}$

$\sf \implies -2+\beta = 3$

$\sf \implies \beta = 3+ 2$

$\sf \implies \beta = 5$

$\rm\pink{\underline{ \mapsto Verification :}}$

Split the middle term of the polynomial.

$\sf \implies x^{2} - 3x -10=0$

$\sf \implies x^{2} - 5x+2x -10=0$

$\sf \implies x(x-5) +2(x-5) =0$

$\sf \implies (x-5)(x+2)=0$

$\sf \implies x = - 2 \: \: \: ; \: \: \: 5$

◼ Since, the two zeroes are = - 2 and 5.

◼ Hence, it was verified.

$\underline{\boxed{\bf{\purple{\therefore The\:another\:zero\:is\:5.}}}}\:\orange{\bigstar}$

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Answer 2

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• polynomial = x² -3x-10
• one zero = -2

_______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• another zero = ???

______________________

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

• compare the eq with $\sf{\underline{\bold{ax^2 + bx + c = 0 }}}$

⠀⠀⠀⠀⠀⠀⠀

☯ a = 1

☯ b = -3

☯ c = - 10

$\sf{\boxed{\purple{sum\:of\:zeros = \dfrac{-b}{a}}}}$

$\sf\implies - 2 + \beta = \dfrac{- ( -3) }{1}$

$\sf\implies - 2 + \beta = + 3$

$\sf\implies \beta = 3 + 2$

$\sf\implies \beta = 5$

$\sf{\red{\boxed{\bold{another \: zero =\: 5 }}}}$

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• another zero of quadratic equation $\sf\bold{x^2 -3x -10 = 0}$ is 5.