Question

Find the quadratic polynomial, some of whose zeros is root 2 and their product is 1/3. Hence find the zeros of the polynomial

Answer 1

Question:

Find the quadratic polynomial, some of whose zeros is root 2 and their product is 1/3. Hence find the zeros of the polynomial.

Answer:

k(3x²-3√2+1).

Step-by-step explanation:

we have Sum of the roots =√2.

and it's product of roots be 1/3.

So,

we have formula,

$\tt \: k( {x}^{2} - sx + p) \\ \\ \leadsto \tt \: k( {x}^{2} - \sqrt{2} x + \frac{1}{3} ) \\ \leadsto\tt k( \frac{3 {x}^{2} - 3\sqrt{2}x + 1 }{3} ). \\ \leadsto \tt k( 3 {x}^{2} - 3\sqrt{2}x + 1 ).$

Some information

$\: \: \: \tt \alpha + \beta = \sqrt{2} \\ \: \: \tt\alpha \times \beta = \frac{1}{3}$

When, given the putting in this expression.

$\\ \tt \: k( {x}^{2} - sx + p)$

S = Sum of roots

P = product of roots.