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What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?
- a)Real
- b)Distinct
- c)Real, Distinct
- d)Complex
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What will be the nature of the zeros of a quadratic polynomial if it c...
The zeros of the quadratic polynomial cut the x-axis at two different points.
∴ b2 – 4ac ≥ 0
Hence, the nature of the zeros will be real and distinct.
∴ b2 – 4ac ≥ 0
Hence, the nature of the zeros will be real and distinct.
Most Upvoted Answer
What will be the nature of the zeros of a quadratic polynomial if it c...
The nature of the zeros of a quadratic polynomial can be determined by considering the discriminant of the polynomial.
The quadratic polynomial can be written in the standard form as ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
The discriminant (D) of the quadratic polynomial is given by the formula D = b^2 - 4ac.
The discriminant provides information about the roots of the quadratic equation:
1. If the discriminant is positive (D > 0), then the quadratic equation has two different real roots. This means that the quadratic polynomial intersects the x-axis at two distinct points. Therefore, the zeros of the quadratic polynomial are real and distinct.
2. If the discriminant is zero (D = 0), then the quadratic equation has two equal real roots. This means that the quadratic polynomial touches the x-axis at a single point. Therefore, the zeros of the quadratic polynomial are real and equal.
3. If the discriminant is negative (D < 0),="" then="" the="" quadratic="" equation="" has="" no="" real="" solutions.="" this="" means="" that="" the="" quadratic="" polynomial="" does="" not="" intersect="" the="" x-axis.="" therefore,="" the="" zeros="" of="" the="" quadratic="" polynomial="" are="" complex="" />
In the given question, it is stated that the quadratic polynomial cuts the x-axis at two different points. This implies that the quadratic equation has two different real roots. Therefore, the zeros of the quadratic polynomial are real and distinct.
Hence, the correct answer is option 'C' - Real, Distinct.
The quadratic polynomial can be written in the standard form as ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
The discriminant (D) of the quadratic polynomial is given by the formula D = b^2 - 4ac.
The discriminant provides information about the roots of the quadratic equation:
1. If the discriminant is positive (D > 0), then the quadratic equation has two different real roots. This means that the quadratic polynomial intersects the x-axis at two distinct points. Therefore, the zeros of the quadratic polynomial are real and distinct.
2. If the discriminant is zero (D = 0), then the quadratic equation has two equal real roots. This means that the quadratic polynomial touches the x-axis at a single point. Therefore, the zeros of the quadratic polynomial are real and equal.
3. If the discriminant is negative (D < 0),="" then="" the="" quadratic="" equation="" has="" no="" real="" solutions.="" this="" means="" that="" the="" quadratic="" polynomial="" does="" not="" intersect="" the="" x-axis.="" therefore,="" the="" zeros="" of="" the="" quadratic="" polynomial="" are="" complex="" />
In the given question, it is stated that the quadratic polynomial cuts the x-axis at two different points. This implies that the quadratic equation has two different real roots. Therefore, the zeros of the quadratic polynomial are real and distinct.
Hence, the correct answer is option 'C' - Real, Distinct.
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What will be the nature of the zeros of a quadratic polynomial if it c...
The zeros of the quadratic polynomial cut the x-axis at two different points.
∴ b2 – 4ac ≥ 0
Hence, the nature of the zeros will be real and distinct.
∴ b2 – 4ac ≥ 0
Hence, the nature of the zeros will be real and distinct.
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What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?a)Realb)Distinctc)Real, Distinctd)ComplexCorrect answer is option 'C'. Can you explain this answer?
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