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Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?

Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE? Correct Answer Only C is true

FORMULA USED:

Sum of roots = (-b/a)

Product of roots = c/a

CALCULATION:

A: In a given quadratic equation ax2 + bx + c = 0

Sum of roots = (-b/a)

Product of roots = c/a

B: Since, we know that imaginary roots always lie in pair.

Which means if one root of a quadratic equation is (p + qi), then other root must be (p – qi)

C: Discriminant of equation: 3x2 + 4x – 5 = 0

D = b2 – 4ac

⇒ 42 – 4 × 3 × (-5)

⇒ 16 + 60

⇒ 76

Which is greater than zero ‘0’. Hence, roots of the equation are all real.

∴, Only C is TRUE.

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