Consider the following statements in respect of the quadratic equation 4(x - p)(x - q) - r2 = 0, where p, q and r are real numbers:
1) The roots are real
2) The roots are equal if p = q and r = 0
Where of the above statements is/are correct ?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
How many real roots does the equation x2 + 3|x| + 2 = 0 have ?
1 only
2 Only
Both 1 and 2
Neither 1 nor 2
Under which one of the following conditions will the quadratic equation x2 + mx + 2 = 0 always have real roots ?
m2 8
m2
If both p and q belong to the set {1, 2, 3, 4}, then how many equations of the form px2 + qx + 1 = 0 will have real roots ?
12
10
7
6
C.
7
Given px2 + qx + 1 = 0 will have real roots, then discriminant (D)
Then, q2 – 4p 0
now, the possible values of (p, q) will be (4, 4), (4, 3),(4, 2), (4, 1), (3, 2), (3, 1), (2, 1)
since, the possible values of (p, q) will be 7
then, option C is correct.
If p and q are the roots of the equation x2 – 30x + 221 = 0, what is the value of p3 + q3 ?
7010
7110
7210
7240
Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30
Consider the following statements:
1) f[g(x)] is a polynomial of degree 3.
2) g[g(x)] is a polynomial of degree 2.
Which of the above statements is/are correct ?
1 only
2 only
Both 1and 2
Neither 1 nor 2