Question

Any genius here plz help me

quadratic polynomial 6x²-7x+2has zeros as Alpha Bita. Now form a quadratic polynomial whose zeroes are 5Aplha and 5Bita.​

Answer 1

Answer

Given -

Quadratic Polynomial 6x²-7x+2 whose zeros are $\alpha$ , $\beta$

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To find -

Quadratic Polynomial whose zeros are $5\alpha$ and$5\beta$

━━━━━━━━━━━━━━━━━━━━━━━━━━

Knowledge required -

Sum of roots = $\frac{ - b}{a}$

Product of root = $\frac{c}{a}$

Equation =

x² - sum of roots(x) + product of roots

where a is coefficient of x² , b is coefficient of x and c is constant.

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Solution.

For polynomial 6x²-7x+2

Sum of roots = $\alpha + \beta = 7/6$

Product of roots = $\alpha \beta = 2/6 = 1/3$

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Let the polynomial whose zeros are $5\alpha$ and $5\beta$ be ax² + bx + c

Sum of roots $= 5\alpha + 5\beta$

$= 5( \alpha + \beta )$

$= 5( \frac{ 7}{6} )$

$= \frac{ 35}{6}$

Product of roots = $5\alpha \times 5\beta$

$= 25( \alpha \beta )$

$= 25 \times 1/3$

$= \frac{25}{3}$

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Equation =

x² - sum of roots(x) product of roots

Equation = ${x}^{2} - \frac{35}{6} x + \frac{25}{3} = 0$

$= 6{x}^{2} - 35x + 50 = 0$

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Thanks

Answer 2

Step-by-step explanation:

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Quadratic Polynomial 6x²-7x+2 whose zeros are \alphaα , \betaβ

━━━━━━━━━━━━━━━━━━━━━━━━━━

To find -

Quadratic Polynomial whose zeros are 5\alpha5α and5\beta5β

━━━━━━━━━━━━━━━━━━━━━━━━━━

Knowledge required -

Sum of roots = \frac{ - b}{a}

a

−b

Product of root = \frac{c}{a}

a

c

Equation =

x² - sum of roots(x) + product of roots

where a is coefficient of x² , b is coefficient of x and c is constant.

━━━━━━━━━━━━━━━━━━━━━━━━━━

Solution.

For polynomial 6x²-7x+2

Sum of roots = \alpha + \beta = 7/6α+β=7/6

Product of roots = \alpha \beta = 2/6 = 1/3αβ=2/6=1/3

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Let the polynomial whose zeros are 5\alpha5α and 5\beta5β be ax² + bx + c

Sum of roots = 5\alpha + 5\beta=5α+5β

= 5( \alpha + \beta )=5(α+β)

= 5( \frac{ 7}{6} )=5(

6

7

)

= \frac{ 35}{6}=

6

35

Product of roots = 5\alpha \times 5\beta5α×5β

= 25( \alpha \beta )=25(αβ)

= 25 \times 1/3=25×1/3

= \frac{25}{3}=

3

25

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Equation =

x² - sum of roots(x) product of roots

Equation = {x}^{2} - \frac{35}{6} x + \frac{25}{3} = 0x

2

−

6

35

x+

3

25

=0

= 6{x}^{2} - 35x + 50 = 0=6x

2

−35x+50=0

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