Question

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Answer 1

Answer:

Question :-

$\mapsto$ One of the zeroes of the polynomial 2x² + 7x - 4 is ?

Given :-

$\mapsto$ The quadratic polynomial is 2x² + 7x - 4.

To Find :-

$\mapsto$ What are the zeroes of a quadratic polynomial.

Solution :-

Given Equation :

$\bigstar\: \: \bf{2x^2 + 7x - 4}$

Let,

$\leadsto \sf p(x) =\: 2x^2 + 7x - 4$

Zero of the polynomial is the value of x where p(x) = 0

By putting p(x) = 0 we get,

$\implies \sf 2x^2 + 7x - 4 =\: 0$

$\implies \sf 2x^2 + (8 - 1)x - 4 =\: 0$

$\implies \sf 2x^2 + 8x - x - 4 =\: 0\: \: \: \bigg\lgroup \small\sf\bold{\pink{By\: splitting\: middle\: term}}\bigg\rgroup$

$\implies \sf 2x(x + 4) - 1(x + 4) =\: 0$

$\implies \sf (2x - 1)(x + 4) =\: 0$

$\longrightarrow \bf 2x - 1 =\: 0$

$\longrightarrow \sf 2x =\: 1$

$\longrightarrow \sf\bold{\red{x =\: \dfrac{1}{2}}}$

$\longrightarrow \bf x + 4 =\: 0$

$\longrightarrow \sf\bold{\red{x =\: - 4}}\: \bigg\lgroup \small\sf\bold{\pink{Zeroes\: can't\: be\: negetive (- ve)}}\bigg\rgroup$

Hence, we have to take x = 1/2.

${\small{\bold{\underline{\therefore\: The\: one\: of\: the\: zeroes\: of\: quadratic\: polynomial\: is\: \dfrac{1}{2}\: .}}}}$

Answer 2

Answer:

To find the zero of 2x

2 +7x−4 is same as solving the equation2x

2 +7x−4=0

⇒2x

2+8x−x−4=0

⇒2x(x+4)−1(x+4)=0

⇒(2x−1)(x+4)=0

⇒(2x−1)=0,(x+4)=0

⇒x= 21,−4

Step-by-step explanation:

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