Question

Que 11. Find a quadratic
polynomial whose zeros are
-2√3 and √3.​

Answer 1

EXPLANATION.

Quadratic polynomial.

Whose zeroes are = -2√3 and √3.

As we know that,

Sum of the zeroes of the quadratic expression.

⇒ α + β = - b/a.

⇒ -2√3 + √3. = -√3.

⇒ α + β = -√3.

Products of the zeroes of the quadratic expression.

⇒ αβ = c/a.

⇒ (-2√3) x (√3) = - 6.

⇒ αβ = - 6.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-√3)x + (-6).

⇒ x² + √3x - 6.

                                                                                                                     

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

$\huge \boxed{ \bf \red{ {x }^{2} + \sqrt{3} x - 6}}$

Step-by-step explanation:

QUESTION :-

Find a quadratic polynomial whose zeros are -2√3 and √3.

________________________

SOLUTION :-

Let the two zeroes as $\alpha \& \beta$

$\bf= > \alpha = - 2 \sqrt{3} \\ \bf = > \beta = \sqrt{3}$

Sum of zeroes (S) = $\alpha + \beta$

=> -2√3 + √3

=> - √3

.

Product of zeroes (P) = $\alpha \beta$

=> -2√3 × √3

=> -2×3

=> - 6

.

To find the quadratic polynomial, we use formula -

x² - (S)x + P

=> x² - (-√3)x + (-6)

=> x² + √3x - 6

So,

the quadratic polynomial is x² + √3x - 6.

Hope it helps.

#Be Brainly :-)