Question

When Aryan was watching a boy playing football, he visualised that the path traced by the ball resembles a parabola, which can be represented by the quadratic polynomial ax2+ bx + c, a ≠0. He further noted that a quadratic polynomial has atmost two real zeroes. If α and β are the zeroes of ax2− bx + c, a ≠0 then calculate α + β.

Answer 1

Answer:

this chapter is pointless,leave it.

Answer 2

Step-by-step explanation.

Given, $f(x)=ax^{2}-bx+c$, a quadratic polynomial with $a\neq 0$.

Since $\alpha$ and $\beta$ are the zeroes of $f(x)$, then

$\quad f(x)=a(x-\alpha)(x-\beta)$

$\Rightarrow ax^{2}-bx+c=ax^{2}-a(\alpha+\beta)x+a\alpha\beta$

Comparing among the coefficients, we get

• $a(\alpha+\beta)=b\Rightarrow \alpha+\beta=\dfrac{b}{a}$
• $a\alpha\beta=c\Rightarrow \alpha\beta=\dfrac{c}{a}$

Answer: $\alpha+\beta=\dfrac{b}{a}$

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