Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i)
$\frac{2}{3} \: and \: \frac{ - 1}{3}$
(ii)
$0 \: and \: - 4 \sqrt{3}$
(iii)
$\frac{ - 3}{2 \sqrt{5} } \: and \: \frac{ - 1}{2}$
(iv)
$\frac{21}{8} \: and \: \frac{5}{16}$


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Answer 1

Answer:

1. 9x²-3x -2 =0

2. x²- 4root3x=0

Step-by-step explanation:

i hope u got my answer

Answer 2

The formula for forming a quadratic equation where α and β are respectively the two zeroes, is => $p(x) = x^{2} -(\alpha +\beta )x+(\alpha \beta ) = 0$

(i)

$\alpha +\beta = \frac{2}{3}\\\alpha \beta =\frac{-1}{3}$  

Putting in formula

$p(x) = x^2 - \frac{2}{3}x - \frac{1}{3} = 0$

       

(ii)

$\alpha +\beta =0\\\alpha \beta =-4\sqrt{3}$

Putting in formula

$p(x) = x^2-0x-4\sqrt{3}=0$

       ⇒ $x^{2} -4\sqrt{3} = 0$

(iii)

$\alpha +\beta =\frac{-3}{2\sqrt{5} } \\\alpha\beta=\frac{-1}{2}$

Putting in formula

$p(x) = x^2 - \frac{-3}{2\sqrt{5} } x- \frac{1}{2} = 0$

(iv)

$\alpha+\beta = \frac{21}{8} \\\alpha\beta=\frac{5}{16}$

Putting in formula

$p(x) = x^2-\frac{21}{8}x+\frac{5}{16} = 0$