Assertion (A): has two real zeroes.𝑥2 + 4𝑥 + 5Reason (R) : A quadratic polynomial can have at the most two zeroes
Question
Assertion (A): has two real zeroes.𝑥2 + 4𝑥 + 5Reason (R) : A quadratic polynomial can have at the most two zeroes
Solution
The assertion (A) and reason (R) are both correct, but the reason (R) is not the correct explanation for assertion (A).
Here's why:
Assertion (A): The quadratic equation x^2 + 4x + 5 has two real zeroes. This is incorrect. The discriminant of a quadratic equation (b^2 - 4ac) determines the nature of its roots. If the discriminant is greater than 0, the equation has two real and distinct roots. If it's equal to 0, the equation has two real and identical roots. If it's less than 0, the equation has two complex roots. For the given equation, the discriminant is (4)^2 - 415 = 16 - 20 = -4, which is less than 0. Therefore, the equation has two complex roots, not real roots.
Reason (R): A quadratic polynomial can have at the most two zeroes. This is correct. A quadratic polynomial can have at most two roots, real or complex. However, this doesn't explain why the given equation would have two real roots, as the nature of the roots depends on the discriminant, not just the degree of the polynomial.
Similar Questions
Make 3 problem questions withSolutions of Rational zeros of polynomial function.
1. Statement A (Assertion): If one zero of the polynomial p(x) = (k² + 4)x² + 9x + 4k is the reciprocal of the other zero then k = 2. Statement B (Reason): If (x - a) is a factor of the polynomial p(x), then a is a zero of p(x). 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 and 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.
Part BConsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A. The other zero must be rational. B. The other zero must be irrational. C. The other zero can be either rational or irrational. D. The other zero must be non-real.
0. (a) Find all solutions of the quadratic equation x2 + 5x + 6 = 0 in Z12.[4 marks](b) Let f (x) = x3 + 9x2 + 1 ∈ Z11[x]. Find three distinct zeroes of f (x) andhence write f (x) as a product of three distinct linear factors.
Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?Responsesf(x)=5x4+x3−x2+x−5𝑓(𝑥)=5𝑥4+𝑥3−𝑥2+𝑥−5f of x is equal to 5 x to the 4th power plus x cubed minus x squared plus x minus 5f(x)=4x5+3x4+2x3+x2+x𝑓(𝑥)=4𝑥5+3𝑥4+2𝑥3+𝑥2+𝑥f of x is equal to 4 x to the 5th power plus 3 x to the 4th power plus 2 x raised to the 3 power plus x squared plus xf(x)=5x6−5x4+5x2−5𝑓(𝑥)=5𝑥6−5𝑥4+5𝑥2−5f of x is equal to 5 x to the 6th power minus 5 x to the 4th power plus 5 x squared minus 5f(x)=4x4−3x3+2x2−1
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