Question

1
24. Find the Quadratic polynomial if the zeroes of it are 2 and1/2
respectively?​

Answer 1

Solution

Given :-

• Zeroes of Quadratic Equation is , 2 & 1/2

Find :-

• Quadratic equations

Explanation

Let

• p & q be zeroes of this Equation

Then,

==> Sum of zeroes (p + q) = 2 + 1/2 =(4+1)/2

==> Sum of zeroes (p + q) = 5/2

and,

==> Product of zeroes (p.q) = 2 . 1/2

==> product of zeros (p.q) = 1

Formula Of Quadratic Equation

$\dag\boxed{\underline{\tt{\red{\:x^2-(p+q)x+(p.q)=0}}}}$

Keep all above Values

==> x² - (5/2)x + 1 = 0

==> (2x² - 5x + 2 )/2 = 0

==> 2x² - 5x + 2 = 0

Hence

• Quadratic equations will be (2x² - 5x + 2 = 0)

__________________

Answer 2

Given:-

• α = 2
• ß = $\sf\dfrac{1}{2}$

To find:-

• the quadratic equation

Formula:-

:$\implies$$\underline\pink{\boxed{\bf p(x) = x²-(α+ß)x+αß}}$

Solution:-

• α+ß = $\sf 2+\dfrac{1}{2}=\dfrac{5}{2}$
• αß = $\sf\dfrac{1}{2}×2=1$

:$\implies$p(x) = $\sf x²-\dfrac{5}{2}x+1$

now, let's multiply the entire equation with 2 so that the denominator gets removed

:$\implies$p(x) = $\sf 2x²-5x+2$