Question

10. Find the zeroes of the polynomial

$p(x) = \sqrt{3} x {}^{2} + 10x + 7 \sqrt{3} .$

Ans:
$- \sqrt{3}$
,
$\frac{ - 7}{ \sqrt{3} }$

Standard:- 10

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Answer 1

Heya !!!

✓3X² + 10X + 7✓3

Coefficient of X² × Constant term = ✓3 × 7✓3 = 21.

We try to split 21 in two parts such that their sum or Subtraction should be equal 10 and product should be equal 21.

Clearly,

3 + 7 = 10

And,

3 × 7 = 21

So,

✓3X² +10X + 7✓3

=> ✓3X² + ( 3 + 7 )X + 7✓3

=> ✓3X² + 3X + 7X + 7✓3

=> ✓3X ( X + ✓3 ) + 7 ( X + ✓3 )

=> ( X + ✓3 ) ( ✓3X + 7 ) = 0

=> ( X + ✓3 ) = 0 OR ( ✓3X + 7 ) = 0

=> X = -✓3 or X = -7/✓3.


Hence,


-✓3 and -7/✓3 are two zeroes of the given polynomial.

★ HOPE IT WILL HELP YOU ★

Answer 2

Hey there !

Solution :

Equation = √3x² + 10x + 7√3

This equation can be factorised by the method of splitting the middle term.

So √ 3 × 7 √ 3 = 21

So we must split the middle term in such a way that their product gives 21 as the result and sum gives 10 as the result

So, 7 and 3 are the perfect terms. So it can be written as :

=> √3x² + 3x + 7x + 7√3 = 0

=> √3x ( x + √3 ) + 7 ( x + √3 ) = 0

=> ( √3x + 7 ) ( x + √3 ) = 0

=> √3x + 7 = 0 ; x + √3 = 0

Solving the two equations we get,

x = - 7 / √3 ; - √3

Hence the zeros p(x) are - 7 / √3 and - √ 3.

Hope my answer helped :-)