Question

polynomial P(x) = x²-4x+3 has zeros Alpha and beta then find alpha²+beta²​

Answer 1

EXPLANATION.

α, β are the zeroes of the quadratic polynomial.

⇒ p(x) : x² - 4x + 3.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = -(-4/1) = 4.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = 3.

To find : α² + β².

⇒ α² + β² = (α + β)² - 2αβ.

Put the values in the equation, we get.

⇒ α² + β² = (4)² - 2(3).

⇒ α² + β² = 16 - 6.

⇒ α² + β² = 10.

                                                                                                               

MORE INFORMATION.

Nature of the roots of the quadratic polynomial.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

(4) If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

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EXPLANATION.

a, B are the zeroes of the quadratic

polynomial.

→ p(x): x² - 4x +3. As we know that,

Sum of the zeroes of the quadratic polynomial.

→ a + B = -b/a.

a+B=(-4/1) = 4.

Products of the zeroes of the quadratic polynomial.

→ aß = c/a.

→ aß = 3.

To find : a² + ß².

a²+ B² = (a + 3)² - 2aß.

Put the values in the equation, we get.

a²+3² = (4)²-2(3).

a²+ 3² = 16-6.

a² + 3² = 10.

MORE INFORMATION.

Nature of the roots of the quadratic

polynomial.

al, if b² - 4ac > (1) Roots are real and unequal, i

(2) Roots are rational and different, if b² 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = O.

(4) If D< 0 Roots are imaginary and unequal or complex conjugate.