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Find zeroes of v²+4√3v-15Also verify relationship …

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Find zeroes of v²+4√3v-15Also verify relationship between the zeroes and the coefficient

Posted by Shivani Rana 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

The given quadratic polynomial is:

v² + 4 $\sqrt 3$ v - 15

By factorizing it we have
v² + 4 $\sqrt 3$ v - 15 = v² + 5 $\sqrt 3$ v - $\sqrt 3$ v - 15
= v(v + 5 $\sqrt 3$ ) - $\sqrt 3$ (v + 5 $\sqrt 3$ )
= (v - $\sqrt 3$ )(v + 5 $\sqrt 3$ )

For zeroes, put the factors equal to zero i.e.,

(v - $\sqrt 3$ )(v + 5 $\sqrt 3$ ) = 0
$\Rightarrow v = \sqrt { 3 } , - 5 \sqrt { 3 }$ are zeroes of the polynomial.

Verification: In the given polynomial a = 1, b = 4 $\sqrt 3$ and c = - 15
Now Sum of the zeroes = $\sqrt { 3 } + ( - 5 \sqrt { 3 } ) = - 4 \sqrt { 3 }$
Also sum of zeroes = $\frac { - b } { a }$ , $\frac { - b } { a } = \frac { - 4 \sqrt { 3 } } { a } = - 4 \sqrt { 3 }$
And product of zeroes = $\sqrt { 3 } \times - 5 \sqrt { 3 }$ = -15
Also, product of zeroes = $\frac { c } { a } = \frac { - 15 } { 1 } = - 15$

ANSWER

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