Advertisements
Advertisements
Question
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Because in this case discriminant is always negative.
For example, in ax2+ bx + c = 0, as b = 0
And a and c have same sign then ac > 0
⇒ Discriminant = b2 – 4ac = – 4 a c < 0
APPEARS IN
RELATED QUESTIONS
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
From the quadratic equation if the roots are 6 and 7.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
The roots of quadratic equation x2 – 1 = 0 are ______.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
