Question

if a and b are the zeros of the polynomial x^2-16 than ab(a+b)is _____​

Answer 1

Answer :....

Solution:

Let the number of cows be x and their legs be 4x.

Let the number of chicken be y and their legs be 2x.

Total number of legs = 4x + 2y.

Total number of heads = x + y.

The number of legs was 14 more than twice the number of heads.

Therefore, 2 × (x + y) + 14 = 4x + 2y.

or, 2x + 2y + 14 = 4x + 2y.

or, 2x + 14 = 4x [subtracting 2y from both sides].

or, 14 = 4x – 2x [subtracting 2x from both sides].

or, 14 = 2x.

or, x = 7 [dividing by 2 on both sides].

Therefore, the number of cows = 7.

Answer 2

$\red{\large\underline{\underline{\mathtt{Question}}}}$

$\textit{If a and b are the zeroes of the polynomials}$

$\textit{Then\:find }$

$\mathtt{ab(a + b)}$

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$\blue{\large\underline{\underline{\mathtt{Solution}}}}$

$\large\underline{To\:find}$

$\mathtt{\rightarrow ab(a + b)}$

$\large\underline{concept:}$

For finding the value of ab(a + b) , we have to first find the value of a and b , by solving the equation x² - 16.

$\large\underline{calculation:}$

$\green{\boxed{x^{2} - 16}}$

We can write 16 as 4².

$\green{\boxed{x^{2} - 4^{2}}}$

We know ,

$\boxed{\mathrm{a^{2} - b^{2} = (a + b)(a - b)}}$

$\green{\boxed{(x + 4)(x - 4)}}$

$\therefore x = 4,-4$

• $a = 4$
• $b = -4$

$\underline{Given\:equation}$

$\green{\boxed{ab(a + b)}}$

Putting the value of a and b in the equation we get,

$\Rightarrow 4 \times (-4) \times (4 + (-4))$

$\Rightarrow 4 \times (-4) \times (0)$

$\Rightarrow 0$

______________________________________

$\green{\boxed{ab(a + b) = 0}}$