Question

Find a quadratic polynomial whose one zero is root 5 and the product of its zeroes is -2 root 5.

Answer 1

Answer:

Step-by-step explanation in Image

Answer 2

Concept:

Sum of Roots and Product of Roots of a Quadratic Equation

If we consider a quadratic equation ax² + bx + c = 0 and α and β to be the roots of the equation, then,

The Sum of roots is given by

α + β = $- \frac{b}{a}$

The Product of roots is given by

α·β = $\frac{c}{a}$

Given:

1) One of the roots of the quadratic polynomial is √5

⇒  let us say α = √5

2) the Product of its roots is -2√5.

⇒ α·β = -2√5

Find:

Find a quadratic polynomial whose one zero is root 5, and the Product of its zeroes is -2 root 5.

Solution:

Let the two roots of the required quadratic polynomial be α and β.

Given, α = √5 and α·β = -2√5

⇒ √5·β = -2√5

⇒ β = -2

So now we got the two zeroes of the quadratic polynomial.

Now the Quadratic equation can be obtained from the roots as follows:

(x - α) · (x - β) = 0

⇒ (x - (√5)) · (x - (-2)) = 0

⇒ (x - √5) · (x + 2) = 0

⇒ x² + 2x - √5x - 2√5 = 0

⇒ x² + (2 - √5)x - 2√5 = 0

∴ The required quadratic polynomial is x² + (2 - √5)x - 2√5

#SPJ3