Question

form a quadratic equation whose one roots is 5 and product of the roots is -2√5​

Answer 1

Answer:

Given the sum of the roots is 2 and the product of the roots is 5.

Therefore, the quadratic equation is given by x

2

− (Sum of the roots)x+ (Product of the roots) =0.

∴x

2

−2x+5=0 is the quadratic equation.

hope it helps you mark me as the brainliest plzz ⭐

Answer 2

Answer

x² + [(2-5√5)/√5] x - 2√4

Given

One root is 5

Product of roots is -2√5​

To Find

Quadratic equation

Solution

Let α , β be roots of the polynomial .

So , let one root , α = 5 ... (1)

A/c , " product of the roots is -2√5​ "

⇒ αβ = -2√5

⇒ (5)β = -2√5  [  From (1)  ]

⇒ β = -2√5 / 5

⇒ β = -2/√5

Since , we have two roots of the equation .So , we have many methods to find quadratic equation .

General Method :

We know that , " Quadratic equation is given by

x² - ( Sum of zeroes )x + ( Product of zeroes )"

⇒ x² - (α+β)x + (αβ)

⇒ x² - (5-2/√5)x + (5×2/√5)

⇒ x² - (5√5-2)x/√5 + 2√5

⇒ x² - [(5√5-2) x]/√5 + 2√5

⇒ x² + [2-5√5]x/√5+2√5

⇒ x² + [(2-5√5)/√5] x - 2√5

Alternate Method :

$\rm (x-\alpha)(x-\beta)=0\\\\\implies \rm (x-5)(x+\dfrac{2}{\sqrt{5}})\\\\\implies \rm x\bigg(x+\dfrac{2}{\sqrt{5}}\bigg)-5\bigg(x+\dfrac{2}{\sqrt{5}}\bigg)\\\\\implies \rm x^2+\dfrac{2x}{\sqrt{5}}-5x-\dfrac{10}{\sqrt{5}}\\\\\implies \bf x^2+\dfrac{(2-5\sqrt{5})x}{\sqrt{5}}-2\sqrt{5}$