Question

The zeroes of the quadratic polynomial x² + 1750x + 175000 are
(1 Point)
(a) both negative
(b) one positive and one negative
(c) both positive
(d) both equal

Answer 1

Question :- The zeroes of the quadratic polynomial x² + 1750x + 175000 are :-

(1 Point)

(a) both negative

(b) one positive and one negative

(c) both positive

(d) both equal

Solution :-

we know that , in quadratic polynomial ax² + bx + c :-

• sum of both roots = (-b/a) .
• Product of roots = (c/a) .

Comparing given quadratic polynomial x² + 1750x + 175000 with ax² + bx + c , we get,

• a = 1
• b = 1750
• c = 175000

Therefore ,

→ sum of both roots = (-b/a) = (-1750/1) = (-1750) = Negative number.

→ Product of roots = (c/a) = (175000/1) = 175000 = Positive number.

Now,

Product of roots is positive , So, either both roots are positive or both roots are negative .

But,

Sum of roots is negative . { sum of two positive can't be a negative number.}

Hence, from both Product and Sum , we conclude that, both roots are negative is the only choice.

∴ Both roots are negative. (Option A.)

Answer 2

Answer:

(a) both negative

Step-by-step explanation:

We know that , in quadratic polynomial ax² + bx + c :-

Sum of both roots = (-b/a) .

Product of roots = (c/a) .

Comparing given quadratic polynomial x² + 1750x + 175000 with ax² + bx + c, we get,

a = 1

b = 1750

c = 175000

Therefore,

→ sum of both roots = (-b/a) = (-1750/1) = (-1750) = Negative number.

→ Product of roots = (c/a) = (175000/1) = 175000 = Positive number.

Now,

Product of roots is positive. So, either both roots are positive or both roots are negative.

But,

Sum of roots is negative. { sum of two positive can't be a negative number.}

Hence, from both Product and Sum , we conclude that, both roots are negative is the only choice.

∴ Both roots are negative. (Option A)

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