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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.

353 Views

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.

150 Views

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.

522 Views

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.

1773 Views

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

We have,
p(x) = abx² + (b² – ac) x – bc
Let α and β be the zeroes of the quadratic polynomial p(x), then
Sum of the zeroes

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equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis over denominator ab end fraction equals fraction numerator ac minus straight b squared over denominator ab end fraction

And product of the zeroes

left parenthesis straight alpha comma space straight beta right parenthesis

equals space fraction numerator Constant space term over denominator Coeff. space of space straight x squared end fraction

equals fraction numerator negative bc over denominator ab end fraction equals negative straight c over straight a

98 Views

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 ?

243 Views

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

566 Views

378. What are parabolas?

74 Views

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

98 Views

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

78 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type

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

Short Answer Type

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