Question

what are the zeros of the quadratic polynomial 3x²- x -
4
​

Answer 1

Given :

• Polynomial 3x²-x-4.

To Find :

• Zeroes of the given polynomial.

Solution :

$\longmapsto\tt\bold{{3x}^{2}-x-4}$

By Splitting Middle Term :

$\longmapsto\tt{{3x}^{2}-(4x-3x)-4}$

$\longmapsto\tt{{3x}^{2}-4x+3x-4}$

$\longmapsto\tt{x(3x-4)+1(3x-4)}$

$\longmapsto\tt{(x+1)(3x-4)}$

• x = -1
• $\dfrac{4}{3}$

So , -1 and 4/3 are the zeroes of polynomial 3x²-x-4...

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Here :

• a = 3
• b = -1
• c = -4

Sum of Zeroes :

$\longmapsto\tt{-1+\dfrac{4}{3}=\dfrac{-b}{a}}$

$\longmapsto\tt{\dfrac{-3+4}{3}=\dfrac{-1}{3}}$

$\longmapsto\tt\bold{\dfrac{-1}{3}=\dfrac{-1}{3}}$

Product of Zeroes :

$\longmapsto\tt{-1\times\dfrac{4}{3}=\dfrac{c}{a}}$

$\longmapsto\tt{-1\times\dfrac{4}{3}=\dfrac{-4}{3}}$

$\longmapsto\tt\bold{\dfrac{-4}{3}=\dfrac{-4}{3}}$

HENCE VERIFIED

Answer 2

$\bf\huge\blue{\underline{\underline{ Question : }}}$

what are the zeros of the quadratic polynomial 3x²- x - 4.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

$\tt{\underline{\underline{\red{ Given\:that:}}}}$

• Polynomial p(x) = 3x² - x - 4

$\tt{\underline{\underline{\green{To\:find:}}}}$

• Zeroes of the Polynomial.

$\tt{\underline{\underline{\orange{Let:}}}}$

◼ We can find out the zeroes of the Quadratic Polynomial by two cases.

➡ ᴄᴀsᴇ - 1 :-

★ By splitting middle term.

$\sf \implies 3x^{2} - x - 4 = 0$

$\sf \implies 3x^{2} + 3x - 4x - 4 = 0$

$\sf \implies 3x(x + 1)-4(x+1)=0$

$\sf \implies (3x-4)(x+1)=0$

$\sf \implies x = \cfrac{4}{3} \: ; - 1$

$\underline{\boxed{\rm{\purple{\therefore Zeroes\:of\:Polynomial = \cfrac{4}{3} \: ; \: - 1}}}}$

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➡ ᴄᴀsᴇ - 2 :-

★ By using co - efficients of the polynomial.

Here

• a = 3
• b = - 1
• c = - 4

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

$\sf \implies \cfrac{-(-1)}{3}$

$\sf \implies \cfrac{1}{3}$

$\sf \rightarrow Product\:of\:the\:zeroes : \alpha\beta = \cfrac{c}{a}$

$\sf \implies \cfrac{-4}{3}$

$\underline{\boxed{\rm{\purple{\therefore Zeroes\:of\:Polynomial = \cfrac{1}{3} \: \: ; \cfrac{ - 4}{3}}}}}$

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