Which constant must be added and subtracted to solve the quadratic equation 9x² + (3/4)x - √2 = 0 by the method of completing the square
a. ⅛
b. 1/64
c. ¼
d. 9/64
Solution:
Given, the quadratic equation is 9x² + (3/4)x - √2 = 0
We have to find the constant to be added and subtracted to solve the quadratic equation by the method of completing the square.
Let y = 3x
Now, (3x)² + (3x)/4 - √2 = 0
y² + (1/4)y - √2 = 0 --------------------- (1)
By using algebraic identity,
(a + b)² = a² + 2ab + b² --------------------- (2)
Comparing (1) and (2),
a² = 1
a = 1
2ab = 1/4
2(1)b = 1/4
b = 1/8
b² = (1/8)² = 1/64
So, y² + (1/4)y - √2 + 1/64 - 1/64 = 0
On rearranging,
y² + (1/4)y + 1/64 - √2 - 1/64 = 0
(y + 1/8)² = √2 + 1/64
Now, (3x + 1/8)² = √2 + 1/64
Therefore, the constant to be added and subtracted is 1/64.
✦ Try This: Which constant must be added and subtracted to solve the quadratic equation 5x² + (3/4)x - 12 = 0 by the method of completing the square
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.1 Problem 7
Which constant must be added and subtracted to solve the quadratic equation 9x² + (3/4)x - √2 = 0 by the method of completing the square, a. ⅛, b.1/64, c.¼, d.9/64
Summary:
The constant should be added and subtracted to solve the quadratic equation 9x² + 3/4 x - √2 = 0 by the method of completing the square is 1/64
☛ Related Questions:
- Which of the following equations has two distinct real roots, a. 2x² - 3√2x + 9/4 = 0, b. x² + x - 5 . . . .
- Which of the following equations has no real roots, a. x² - 4x + 3√2 = 0, b. x² + 4x - 3√2 = 0, c. x . . . .
- (x² + 1)² - x² = 0 has, a. four real roots, b. two real roots, c. no real roots, d. one real root
visual curriculum