Question

Find a quadratic polynimial whose sum and product of its zeroes are 4 and 1

Answer 1

Answer:

x^2-4x+1

Step-by-step explanation:

Sum of zeroes=4

Product of zeroes=1

Required polynomial=x^2-Sx+P

=x^2-4x+1

Answer 2

Sum and product of zeros are 4 and 1

________ [ GIVEN ]

• We have to form/find a quadratic polynomial.

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• Lat one zero be $\alpha$ = 4

And

• Another zero be $\beta$ = 1

Now ..

Sum of zeros = $\alpha$ + $\beta$

=> 4 + 1 = 5

Product of zeros = $\alpha$$\beta$

=> 4 × 1 = 4

We know that ..

x² - (Sum of zeros)x + Product of zeros

=> x² - (5)x + 4

=> x² - 5x + 4

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x² - 5x + 4 is a quadratic polynomial whose zeros are 4 and 1.

____________ [ ANSWER ]

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✡ $\underline{Verification}$ :

→ x² - 5x + 4 = 0

→ x² - 4x - x + 4 = 0

→ x(x - 4) - 1(x - 4) = 0

→ (x - 1) (x - 4) = 0

→ x = 1, 4

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