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Polynomials

Short Answer Type

331.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

t² - 15

919 Views

332. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

3 straight x squared minus straight x minus 4.

167 Views

333. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

space 1 fourth comma space minus 1

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334. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

square root of 2 comma space 1 third

684 Views

335. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
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Let the quadratic polynomial be ax² + bx + c, and its zeroes be α and β. Then,

straight alpha plus straight beta space equals space square root of 0 space space space rightwards double arrow space space minus straight b over straight a equals 0 space space rightwards double arrow space minus straight b space equals space 0

and

αβ space equals space square root of 5 space space space space rightwards double arrow space space straight c over straight a space equals space square root of 5 space space space rightwards double arrow space space straight c space equals space straight a. square root of 5

straight a equals 1 comma space space then space straight b space equals space 0 space and space straight c space equals space square root of 5.

So, quadratic polynomial which fits the given condition is

straight x squared plus 0. straight x plus square root of 5 space or space straight x squared plus square root of 5

249 Views

336. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
1, 1

274 Views

337. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

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266 Views

338. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
4, 1

163 Views

339. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

172 Views

340. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

128 Views