Math, asked by divyansh2june2013, 2 months ago

if x= -1/2 is a zero of the polynomial f(x) = 2x²-3x+7a find the value of a​

Answers

Answered by singhanshika1102
1

Answer:

-2/7 is the answer

Step-by-step explanation:

2*-1/2*-1/2-3*-1/2+7a=0

1/2+3/2+7a=0

2+7a=0

7a=-2

a=-2/7

Answered by Anonymous
22

Solution -

We have a polynomial f(x) = 2x² - 3x + 7a

It is given that -1/2 is a zero of the given polynomial.

Since, it is the zero of polynomial.

It means x = -1/2 is the perfect solution of the polynomial.

Now, we put

  • x = -1/2

\tt\dashrightarrow{f(x) = 2x^2 - 3x + 7a}

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2}\bigg) = 2 \bigg( \dfrac{-1}{2} \bigg)^2 - 3 \bigg( \dfrac{-1}{2} \bigg) + 7a }

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2}\bigg) = 2 \bigg( \dfrac{1}{4} \bigg) + \dfrac{3}{2} + 7a}

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2} \bigg) = \dfrac{1}{2} + \dfrac{3}{2} + 7a}

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2} \bigg) = \dfrac{1 + 3}{2} + 7a}

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2} \bigg) = \dfrac{4}{2} + 7a}

\tt\dashrightarrow{f \bigg( \dfrac{-1}{2} \bigg) = 2 + 7a}⠀⠀...[1]

Now, it is given that x = -1/2 is a zero of the given polynomial. Therefore,

  • Put f(x) = 0

\tt\longmapsto{f \bigg( \dfrac{-1}{2} \bigg) = 0}

\tt\longmapsto{2 + 7a = 0}⠀⠀\bigg\lgroup{From\: [1]} \bigg\rgroup

\tt\longmapsto{7a = -2}

\frak\longmapsto{\underline{\boxed{\pink{a = \dfrac{-2}{7}}}}}

\: \: \: \: \: \: \: \: \: \:\underline{\sf{\therefore \: Value\: of\: a\: is\: \dfrac{-2}{7}}}

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