Question

Form a quadratic equation sum of whose roots is 5 and one of the roots is 5−3√3/2.​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

Let 'm' and 'n' be the roots ∴m=3+25 and n=3−25

Sum of the roots =m+n=3+25+3−25∴m+n=6

Product of the roots =mn=(3+25)(3−25)=(3)2−(25)2=9−20∴mn=−11

x2−(m+n)x+mn=0∴x2−6x−11=