Quadratic Equation
Only available for you
The roots of a quadratic equation ax2 + bx + c = 0 (where a ≠ 0) can be given as:
$$\frac{-b\:\pm \sqrt{b^2-4ac}}{2a}$$
- D = b2 − 4ac is also known as the discriminant of quadratic equation.
- For roots;
- (i) D> 0 happens when the roots are real and distinct
- (ii) For real and coincident roots, D = 0
- (iii) D< 0 happens in the case when the roots are non-real
- If α and β are the two roots of the equation ax2 + bx + c then,
$$α + β = {{-b}\over{a}}$$. and $$α × β = {{c}\over{a}}$$. - If the roots of a quadratic equation are α and β, the equation will be
(x − α)(x − β) = 0.
2 How many distinct positive integer-valued solutions exist to the equation (x2 - 7x + 11)(x2 - 13x + 42) = 1?
A
6
B
2
C
4
D
8
4 (3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be the value of b?
A
2
B
√2
C
-√2
D
All of the above
5 Let x3- x2 + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true
A
b=2,c=2
B
b=1,c=1
C
b= -1,c = 1
D
b= -1,c= -1
7 If f(y) = x2 + (2p + 1)x + p2 - 1 and x is a real number, for what values of ‘p' the function becomes 0?
A
p > 0
B
p > -1
C
p ≥ \\frac{-5}{4}\\)
D
p ≤ \\frac{3}{4}\\)
8 Let A be a real number. Then the roots of the equation x2 - 4x – log2A = 0 are real and distinct if and only if
A
A < \\frac{1}{16})
B
A > \\frac{1}{8})
C
A > \\frac{1}{16})
D
A < \\frac{1}{8})
