Question

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Answer 1

Step-by-step explanation:

Question:-

If α and β are the zeroes of the quadratic polynomial f(x) = x² - p(x + 1) - c. Find the value of (α+ 1) (β + 1).

Solution:-

Given polynomial = x² - p(x + 1) - c

= x² - px - p - c

Comparing the polynomial with ax² + bx + c

Here:-

• a = 1 , b = -p , c = - p - c

Sum of zeroes = $\rm\dfrac{-b}{a}$

→ α + β = $\rm\dfrac{-(-p)}{1} = p$

Product of zeroes = $\rm\dfrac{c}{a}$

→ αβ = $\rm\dfrac{-p - c}{1} = -p - c$

We have :-

• α + β = p

• αβ = - p - c

Now, the value of (α + 1) (β + 1)

⇢ (α + 1) (β + 1)

⇢ (αβ) + (α + β) + 1

⇢ - p - c + p + 1

⇢ p - p + 1 - c

⇢ 1 - c

∴ (α + 1) (β + 1) = 1 - c

Answer 2

Answer:

a+1-b+1=c-1

Step-by-step explanation:

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