A): The equation ax² + bx + c = 0

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Q.
Assertion (A): The equation $a x ² + b x + c = 0$ has two real roots always.

Reason (R): The sum of roots of $a x ² + b x + c = 0 i s - b / a$ and the product of roots is c/a.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

Ans.
(4)

For a quadratic equation $a x ² + b x + c = 0,$ we know:
(i) $I f b ² - 4 a c > 0,$ then the equation has two real and distinct roots.
(ii) $I f b ² - 4 a c = 0$ , then the equation has two real and equal roots.
(iii) $I f b ² - 4 a c < 0$ , then the equation has no real roots.

And, sum of roots = −b/a and product of roots = c/a.
Hence, Assertion (A) is false but Reason (R) is true.

Solution

Q.
Assertion (A): The equation $a x ² + b x + c = 0$ has two real roots always.

Reason (R): The sum of roots of $a x ² + b x + c = 0 i s - b / a$ and the product of roots is c/a.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

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Solution

Q. Assertion (A): The equation ax² + bx + c = 0 has two real roots always. Reason (R): The sum of roots of ax² + bx + c = 0 is −b/a and the product of roots is c/a.

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true

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Q.
Assertion (A): The equation $a x ² + b x + c = 0$ has two real roots always.

Reason (R): The sum of roots of $a x ² + b x + c = 0 i s - b / a$ and the product of roots is c/a.