Question

3. If zeroes of p(x) = 2x2 - 7x + k are reciprocal of each other, then value of k is
4. Sum and product of zeroes of a quadratic polynomial are 0 and√15 is respectively. Find the
quadratic polynomial.​

Answer 1

Answer:

the answer is case equal to 1.5

Answer 2

(i) The value of k is 2.

(ii) The quadratic polynomial is x² + √15.

Given:

(i) The zeroes of p(x) = 2x² - 7x + k are reciprocal of each other.

(ii) The sum and product of zeroes of a quadratic polynomial are 0 and√15 respectively.

To Find: (i) The value of k.

             (ii) The quadratic polynomial.​

Solution:

(i) Let the zeroes be a and b.

   Now, it is said that the zeroes are reciprocals of each other, so we can say that, b = 1/a.

We know that for a polynomial, ax² - bx + c = 0,

• Sum of the zeroes = - b/a
• Product of the zeroes = c/a

Coming to the numerical, we are given the polynomial,

                 2x² - 7x + k = 0,

So from the given information, we can say that,

   a + 1/a = 7/2                                ....(1)

   a × 1/a = k/2                                ....(2)

Using (2),

⇒ a × 1 / a = k / 2

⇒ k / 2 = 1

⇒ k = 2

Hence, the value of k is 2.

(ii) We know that the structure of a polynomial can be given by,

        f(x) = x² - Sx + P                      .......(1)

    where, S = sum of the zeroes, P = product of the zeroes.

Coming to the numerical, we are given;

   The sum of zeroes (S) of a quadratic polynomial = 0

   The  product of zeroes (P) of a quadratic polynomial = √15

So, from (1) we can say that,

    f(x) = x² - Sx + P

⇒  f(x) = x² - 0 × x + √15

⇒ f(x) = x² + √15

Hence, the quadratic polynomial is x² + √15.

Compiling the answers, we get;

(i) The value of k is 2.

(ii) The quadratic polynomial is x² + √15.

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