English

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.

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

MCQ
True or 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

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Quadatric Euation - Exercise 4.2 [Page 38]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 10
Chapter 4 Quadatric Euation
Exercise 4.2 | Q 2.(vi) | Page 38

RELATED QUESTIONS

Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.


Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.


The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.


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 the following quadratic equation:

4x2 – 2(k + 1)x + (k + 4) = 0


Find the values of k for which the roots are real and equal in the following equation:

kx(x – 2) + 6 = 0


Find the values of k for which the given quadratic equation has real and distinct roots:

kx2 + 6x + 1 = 0


If the equation \[\left(1 + m^2 \right) x^2 + 2mcx + \left(c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).


Determine the nature of the roots of the following quadratic equation : 

2x2 -3x+ 4= 0 


Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.


In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3


Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0


Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0


Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0


Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0


The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:


Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.


If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.


If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.


Which of the following equations has imaginary roots?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×