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Polynomials

Short Answer Type

371. If x = 4, is a zero of the polynomial x² – 5x + 4, write a factor of the given polynomial.

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Long Answer Type

372. If α, β are the zeroes of the polynomial p(x) = 4x² + 3x + 7. Find the value of

space space 1 over straight alpha plus 1 over straight beta.

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Short Answer Type

373. If one root of the polynomial p(x) = 5x² + 13x + K is reciprocal of the other. Find the value of K.

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Long Answer Type

374.

If sum of the squares of zeroes of the quadratic polynomial p(x) = x² – 8x + K is 40, find the value of K.

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375. Find the sum and product of the zeroes of the quadratic polynomial:
p(x) = abx² + (b² – ac) x – bc.

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Short Answer Type

376. The sum and product of the zeroes of quadratic polynomial are –1/2 and –3 respectively. What is the quadratic polynomial ?

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377. The graph of y = f(x) is given below. Find the number of zeroes of f(x).

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378. What are parabolas?

For any quadratic polynomial ax² + bx + c = 0, a ≠ 0, the graph of the corresponding equation y = ax² + bx + c has one of the two shapes either open upwards like this ∪ or downwards like this ∩ depending on whether a > 0 or a < 0. These curves are called parabolas.

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379. In Fig. 2.4, the graph of a polynomial p{x) is given. Find the zeroes of the polynomial.

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380. Write the zeroes of the polynomial x²+2x+1.

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