Paragraph: Consider the following for the next two (02) items that follow: A quadratic equation is given by (3+2 2 ) x^2-(4+2 3 ) x+(8+4 3 )=0 Question: What is the HM of the roots of the equation?

Correct answer: B. 4 (3+2 2 ) x^2-(4+2 3 ) x+(8+4 3 )=0 If roots are α, =(2 α β)/(α+β)= 2( 8+4 3 3+2 2 ) 4+2 3 (3+2 2 ) = 2(8+4 3 ) 4+2 3 =4 (4+2 3 ) 4+2 3 =4

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Quadratic Equation

NDA 2023 · Mathematics · Quadratic Equation

Paragraph: Consider the following for the next two (02) items that...

Paragraph: Consider the following for the next two

(02)

items that follow: A quadratic equation is given by

(3+2 \sqrt{2}) x^2-(4+2 \sqrt{3}) x+(8+4 \sqrt{3})=0

Question: What is the HM of the roots of the equation?

Options

A $2$
B $4$
C $2 \sqrt{2}$
D $2 \sqrt{3}$

Correct answer

B. $4$

Step-by-step solution

(3+2 \sqrt{2}) x^2-(4+2 \sqrt{3}) x+(8+4 \sqrt{3})=0

If roots are

\alpha, \beta\mathrm{HM}=\frac{2 \alpha \beta}{\alpha+\beta}=\frac{2\left(\frac{8+4 \sqrt{3}}{3+2 \sqrt{2}}\right)}{\frac{4+2 \sqrt{3}}{(3+2 \sqrt{2})}}=\frac{2(8+4 \sqrt{3})}{4+2 \sqrt{3}}=4 \frac{(4+2 \sqrt{3})}{4+2 \sqrt{3}}=4

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

For a given k , what is the minimum value of x^2+kx+k^2 ? NDA 2026 If the highest degree coefficient is equal to 1 , then what is the total number of… NDA 2026 Let α and β be the roots of the quadratic equation x^2-2bx+c^2=0 where b , c are positive… NDA 2026 Consider the following statements : I. x + x+1=0 has two irrational roots. II. 5 x -x-4=0… NDA 2026 For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such… NDA 2025 For the following two (02) items: Let α and β be the roots of the quadratic equation x^2… NDA 2025 For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such… NDA 2025 If one root of the equation x^2 - kx + k = 0 exceeds the other by 2 3 , then which one of… NDA 2025 For the following two (02) items: Let α and β be the roots of the quadratic equation x^2… NDA 2025 If x = (1111)_2 , y = (1001)_2 and z = (110)_2 , then what is x^3 - y^3 - z^3 - 3xyz… NDA 2025 If x^2 - x + 1 = 0 , then what is (x - (1)/(x))^2 + (x - (1)/(x))^4 + (x - (1)/(x))^8… NDA 2025 If x + (5)/(y) = 4 and y + (5)/(x) = -4 , then what is (x + y) equal to? NDA 2025 For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx +… NDA 2025 For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx +… NDA 2025 If n is a root of the equation x^2+p x+m=0 and m is a root of the equation x^2+p x+n=0… NDA 2024 The roots of the equation 7 x^2-6 x+1=0 are α and β , where 2 α and 2 β are the angles of… NDA 2024 Full Quadratic Equation list Quadratic Equation JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs