Question

Find a quadratic pilynomials if the zeroes of it are 2 and-1/3​

Answer 1

Step-by-step explanation:

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Answer 2

Question:

Find a quadratic polynomials if the zeroes of it are 2 and-1/3

To find:

To find the quadratic polynomial.

Answer:

$The \: equation \: is \: \underline{ \: \bold{3 {x}^{2} + 5x - 2 = 0} \: }$

Given data:

Their roots are given,

$\alpha = 2$

$\beta = \frac{ - 1}{3}$

Step-by-step explanation:

If roots are given the equation will be,

$\boxed{ {x}^{2} + ( \alpha + \beta )x + \alpha \beta = 0}$

${x}^{2} + \big(2 - \frac{1}{3} \big)x + \big(2 \times \frac{ - 1}{3} \big) = 0$

${x}^{2} + \frac{5}{3}x - \frac{2}{3} = 0$

Multiplying 3 on both sides,

$(3 \times {x}^{2}) +( 3 \times \frac{5}{3}x) -(3 \times \frac{2}{3}) = 0$

$\implies\boxed{3 {x}^{2} + 5x - 2 = 0}$

Rule:

If the roots α and β are given the required equation is,

x² + (α + β)x + αβ = 0