Math, asked by hamingwithdarkknight, 11 months ago

if a and b are zeroes of the quadratic polynomial 2x2 + 3x - 6, then find the values of (i) a− b

Answers

Answered by Anonymous
8

\huge\text{\underline{Answer}}

\sf{\underline{Given }}

a and b are the zeroes of the given quadratic polynomial.

By using relationship between the zeroes and the coefficient of quadratic polynomial.

\boxed{\sf{ \alpha   + \beta  =  \frac{ - b}{a} }}

\boxed{\sf{ \alpha  \beta  =  \frac{c}{a} }}

Where alpha and betta are zeroes of polynomial.

\implies \bold{a + b =  \frac{ - 3}{2}  }

\implies \bold{ ab =  \frac{ - 6}{2} }

\implies \bold{ab = -3}

Now using the suitable identity,

\boxed{\sf{{(a  - b)}^{2}  =  {(a + b)}^{2}  - 4ab}}

\implies \bold{ {(a - b)}^{2}  =  { (\frac{-3}{2} )}^{2}  - 4 \times  - 3}

\implies \bold{{(a - b)}^{2}  =  \frac{9}{4}  +  \frac{12}{1} }

\implies \bold{ {(a  -  b)}^{2}  =  \frac{57}{4} }

\implies \bold{  (a - b) =  \frac{ \sqrt{57} }{2}}

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