QUADRATIC EQUATION (CLASS10) IMPORTANT QUESTIONS

                                        

Important Questions for Class 10 Maths Chapter 4

KRISHAN KUMAR

QUADRATIC EQUATION

What is Quadratic Equation?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α,β).

The quadratic equation will always have two roots. The nature of roots may be either real or imaginary.

Quadratic Equation Formula

The solution or roots of a quadratic equation are given by the quadratic formula:

(α, β) = [-b ± √(b2 – 4ac)]/2ac

 Nature of roots:

• D > 0, roots are real and distinct (unequal)
• D = 0, roots are real and equal (coincident)
• D < 0, roots are imaginary and unequal

Relationships between Coefficient and Roots of  Quadratic Equation

If α and β are roots of a Quadratic Equation ax2 + bx + c then,

• α + β = -b/a
• αβ = c/a

Question 1.
Find the roots of the equation x2 – 3x – m (m + 3) = 0, where m is a constant.

Question 2.
Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots

Question 3..
Find the value of m so that the quadratic equation mx (x – 7) + 49 = 0 has two equal roots. 

Question 4.
Find the value(s) of k so that the quadratic equation x2 – 4kx + k = 0 has equal roots.

                                                                  Question5

Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.

Question 6.

Find the value of p for which the roots of the equation px(x – 2) + 6 = 0, are equal. 

Question 7.
Solve the quadratic equation 2x2 + ax – a2 = 0 for x. 

Question 8.
Find the values of p for which the quadratic equation 4x2 + px + 3 = 0 has equal roots

Question 9

Solve the following quadratic equation for x: 4x2– 4a2x + (a4 – b4) = 0

ans

∴ x = 

a2−b22 or x = a2+b22

Question 10

Solve the following quadratic equation for x: 9x2 – 6b2x – (a4 – b4) = 0 

ans:

                                                      Question 11
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. 

                                                      Question 12.
Solve for x: 2x+9−−−−−√ + x = 13. 

                                                       Question 13.
Solve for x: 6x+7−−−−−√ – (2x – 7) = 0 

                                                         Question 14.
find the roots of the following quadratic equation: 23–√x2 – 5x + 3–√ = 0

                                                        Question 15.
For what values of k, the roots of the quadratic equation (k + 4)x2 + (k + 1)x + 1 = 0 are equal? 

                                                         Question 16.
For what value of k, are the roots of the quadratic equation y2 + k2 = 2 (k + 1)y equal?

                                                      Question 17.
Solve for x: 3–√x2 – 223−−√x – 23–√ = 0 

                                                        Question 18.
Solve the equation 3x+1−12=23x−1; x ≠ -1, x ≠ 13 for x. 

                                                        Question 19.
Solve for x: 2xx−3+12x+3+3x+9(x−3)(2x+3) = 0, x ≠ 3, −32

                           

                                                        Question 20
Solve for x: x−1x−1+x−2x+2=4−2x+3x−2; x ≠1, -2, 2

hope u like the questions ..........

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