Question

If a and B are the zeros of the polynomial q(x)= x2 - 2x+6 then find the value
of a2 + B2.​

Answer 1

EXPLANATION.

→ a and b are the zeroes of the polynomial

q(x) = x² - 2x + 6.

→ To find the value of a² + b².

→ Sum of the zeroes of the quadratic equation.

→ a + b = -b/a

→ a + b = 2 .......(1).

→ Products of the zeroes of the quadratic

equation.

→ ab = c/a

→ ab = 6 ..........(2).

→ a² + b² = ( a + b)² - 2ab

→ ( 2)² - 2(6)

→ 4 - 12.

→ -8

Answer 2

Answer :-

✯ Given :-

• If α and β are the zeros of the polynomial where q(x) = x² - 2x + 6.

✯ To Find :-

• What is the value of α² + β².

✯ Solution :-

⋆ Given :-

$\leadsto$ q(x) = x² - 2x + 6

↣ where, a = 1, b = - 2, c = 6

If α and β are the zeros of the polynomial of q(x) then,

➠ α + β = - $\dfrac{b}{a}$ = -(-2) = 2

➠ αβ = $\dfrac{c}{a}$ = 6

❖ The value of α² + β² is,

⇒ α² + β²

⇒ (α + β)² - 2αβ

⇒ (2)² - 2(6)

⇒ 4 - 12

➥ - 8

$\therefore$ The value of α² + β² is $\boxed{\bold{\small{-\: 8}}}$

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