Is the following statement ‘True’ or ‘False’? Justify your answer. If in a quadratic equation the coefficient of x is zero, then the quadratic equation has no real roots
Solution:
Given, the quadratic equation has the coefficient of x as zero.
We have to determine if the equation has no real roots.
Discriminant = b² - 4ac
Let us consider the equation px² + 0x + c = 0
Case 1) when p is positive and c is negative
b² - 4ac = 0 - 4(p)(-c)
= + 4pc > 0
Therefore, the roots will be distinct and real.
Case 2) when p is negative and c is positive
b² - 4ac = 0 - 4(-p)(c)
= + 4pc > 0
Therefore, the roots will be distinct and real.
Case 3) when p and c both are positive
b² - 4ac = 0 - 4(p)(c)
= -4pc < 0
Therefore, the root will be unreal.i.e.,no real roots.
Case 4) when p and c both are negative
b² - 4ac = 0 - 4(-p)(-c)
= -4pc < 0
Therefore, the roots will be unreal.i.e., no real roots.
Case 5) when p or c is zero,
b² - 4ac = 0 - 4(p)(0) or 0 - 4(0)(c)
= 0
Therefore, the roots will be equal.
Therefore, it is clear that if the coefficients of p and c are of opposite sign or if one of p or c is zero, the roots will be real or equal.
✦ Try This: Is the following statement “True” or “False”? Justify your answer. If in a quadratic equation the constant is zero, then the quadratic equation has no real roots
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Sample Problem 2
Is the following statement ‘True’ or ‘False’? Justify your answer. If in a quadratic equation the coefficient of x is zero, then the quadratic equation has no real roots
Summary:
If in a quadratic equation the coefficient of x is zero, then the quadratic equation has no real roots. The statement is false.
☛ Related Questions:
- Which of the following equations has 2 as a root, a. x² - 4x + 5 = 0, b. x² + 3x - 12 = 0, c. 2x² - . . . .
- If 1/2 is a root of the equation x² + kx - 5/4 = 0, then the value of k is, a. 2, b. - 2, c. ¼, d. 1 . . . .
- Which of the following equations has the sum of its roots as 3, a. 2x² - 3x + 6 = 0, b. -x² + 3x - 3 . . . .
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