If one root of the quadratic equation is 3-2-5- then write and root of the equation-

Given that one root of the quadratic equation is 3 2 √(5) Since the coefficients of the quadratic equation are real , the other root must be 3+2 √(5) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Quadratic Equations

If one root o...

Question

If one root of the quadratic equation is $3 - 2 \sqrt{5}$ , then write and root of the equation.

Open in App

Solution

Given that one root of the quadratic equation is $3 - 2 \sqrt{5}$
Since the coefficients of the quadratic equation are real , the other root must be $3 + 2 \sqrt{5}$
The sum of roots will be $3 - 2 \sqrt{5} + 3 + 2 \sqrt{5} = 6$
The product of roots will be $(3 + 2 \sqrt{5}) (3 - 2 \sqrt{5}) = 9 - 20 = - 11$
So the quadratic equation will be $x^{2} - 6 x - 11 = 0$

Suggest Corrections

Similar questions

Q. If one of the roots of the quadratic equation is

(2 + \sqrt{3})

then the quadratic equation is

If one of the roots of a quadratic equation is 5 and the product of their roots is -165, then the quadratic equation is :

Q. If

- 5

is one root of quadratic equation

2 x^{2} + p x - 15 = 0

and roots of quadratic equation

p (x^{2} + x) + k = 0

is equal, then find the value of

k

Q. If one of the roots of the real quadratic equation is

(2 - \sqrt{3})

, then the equation is

Q. If one root of a quadratic equation with rational coefficient is

(\begin{matrix} \frac{3 \sqrt{5}}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} \end{matrix})

then quadratic equation is

Join BYJU'S Learning Program

If one root of the quadratic equation is 3−2√5, then write and root of the equation.

If one root of the quadratic equation is $3 - 2 \sqrt{5}$ , then write and root of the equation.