Question

Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

To check if Reason (R) explains Assertion (A), ask: "Does the truth of R guarantee the truth of A?"
Since a quadratic polynomial can have at most 2 zeroes (which includes 0 or 1 zero), it doesn't automatically mean our given polynomial MUST have 2 zeroes.
Therefore, R does not fully explain A, leading to option (B).

Answer 1

The Correct Option is B

Step 1: Check Assertion (A) using the quadratic formula instead of factorising.
For $p(y)=y^2+4y+3$, the quadratic formula gives $y=\dfrac{-4\pm\sqrt{16-12}}{2}=\dfrac{-4\pm2}{2}$, so $y=-1$ or $y=-3$. That's two real zeroes, so A is true.
Step 2: Check Reason (R) by thinking about the discriminant.
R claims a quadratic can have at most two zeroes, which is a general true fact about degree-2 polynomials. But it doesn't say why THIS particular polynomial has exactly two zeroes, that depends on its discriminant being positive: $D=4^2-4(1)(3)=4>0$.
Step 3: Decide whether R explains A.
Since R only sets an upper limit and never mentions the discriminant that actually decides how many zeroes this polynomial has, R is true but does not correctly explain A.
\[ \boxed{\text{Option (B): both A and R are true, R does not explain A}} \]