The zeroes of the quadratic polynomial p(x)= x2 + kx + k , k is not = to 0: A) - Maths - Polynomials

Question

The zeroes of the quadratic polynomial p(x)= x2 + kx
+ k , k is not = to 0:
A) are always equalB)are always unequalC) both cannot be
positiveD) both cannot b negative
ans is option Ce
xplain how

S. Usha Rani · Accepted Answer

We know that, to have equal/same zeroes,

D = 0

$\Rightarrow k^{2} - 4 k = 0 \Rightarrow k (k - 4) = 0 \Rightarrow k = 0 or k = 4$

Since k is not zero, we get k=4. So, it has equal zeros only when k=4 not always. (So option A is false).

Since it has equal zeros at k=4, option B (the roots are unequal always) is false.

By quadratic formula, we have

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- k \pm \sqrt{k^{2} - 4 k}}{2}$

Here, let us assume some value for 'k' where square root of k^2-4k exists. Let us take k=-5. Then we get

$x = \frac{5 \pm \sqrt{25 + 20}}{2} = \frac{5 \pm \sqrt{45}}{2} = \frac{- 5 \pm 6.7}{2} = \frac{- 5 + 6.7}{2} 0 r \frac{- 5 - 6.7}{2} = 0.85 o r - 5.85$

By seeing this example we can say that both zeros cannot be negative always.

-2

The zeroes of the quadratic polynomial p(x)= x2 + kx + k , k is not = to 0: A) are always equalB)are always unequalC) both cannot be positiveD) both cannot b negative ans is option Ce xplain how

The zeroes of the quadratic polynomial p(x)= x² + kx + k , k is not = to 0:

A) are always equalB)are always unequalC) both cannot be positiveD) both cannot b negative

ans is option Ce

xplain how