Math, asked by preeta9399, 10 months ago

plzz answer this question....... This is the question of class 10 exercise 2.2
those who will answer will be Mark as brainlist..​

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Answered by ShahnwazHussain1
6

\underline{\boxed{\tt{\huge{\red{AnSwEr}}}}}

&lt;marquee direction="left" behavior="slide" scrolldelay="5"&gt; </strong><strong>Step-by</strong><strong>-step</strong><strong> explanation</strong><strong>:</strong><strong>-</strong><strong>&lt;/marquee&gt;

We have,

 \implies \:  {x}^{2}  - 2x - 8 \\ \implies \:  {x}^{2}  - 4x + 2x - 8 \\ \implies \: x(x - 4) + 2(x - 4) \\ \implies \: (x + 2) \: (x - 4) \\  \\  if \: f(x) = 0 \\ then. \: x + 2 = 0 \\ \: \implies x =  - 2 \\  \\ if \: f(x) = 0 \\ then \: x - 4 = 0 \\ \implies \: x = 4.

\huge{\therefore x = -2, 4}}

\huge\pink{\mid{\underline{\overline{\tt Verify:-}}\mid}}

Let \:  - 2 \: be \:  \alpha and \: 4 \: be \:  \beta . \\  \implies \:  \alpha  +  \beta  =  \frac{ - b}{a}  \\ \implies \:  - 2 + 4 =  - 2(- 2) \\ \implies \: 2 = 2. \\ (ii) \: Product of Zero \\  \implies \:  \alpha  \times  \beta  =  \frac{c}{a}  \\ \implies \:  - 2 \times 4 =  - 8 \\ \implies - 8 =  - 8 \\ \: \:verified

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Answered by sourya1794
2

Correct Question:-

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients

  • i) x² - 2x -8

Solution:-

\rm\:{x}^{2}-2x-8

\rm\:={x}^{2}-4x+2x-8

\rm\:=x(x-4)+2(x-4)

\rm\:=(x+2)\:(x-4)

so,

The value of x² - 2x - 8 is zero

Now,

\rm\implies\:x+2=0

\rm\implies\:x=0-2

\rm\implies\:x=-2

And,

\rm\implies\:x-4=0

\rm\implies\:x=0+4

\rm\implies\:x=4

∴ The zeros of x² - 2x - 8 are -2 and 4

Now,

Sum of zeros = \rm\:-2+4=2=\dfrac{-(-2)}{1}=\dfrac{(-coefficient\:of\:x)}{(coefficient\:of\:{x}^{2})}

Product of zeros =\rm\:(-2)\times\:4=-8=\dfrac{-8}{1}=\dfrac{constant\:term}{(coefficient\:of\:{x}^{2})}

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