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Polynomials

Long Answer Type

411. Find the zeroes of the quadratic polynomial x² – 5x + 6, and verify the relationship between the zeroes and the coefficients.

512 Views

412. Find the zeroes of x² –2 and verify the relationship between the zeroes and the coefficients.

We have

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So, the value of

straight x squared minus 2

is zero when

left parenthesis straight x plus square root of 2 right parenthesis equals 0 space space space space or comma space space space straight x minus square root of 2 equals 0.

i.e. when

straight x equals negative square root of 2 space space space space or space straight x equals square root of 2

Therefore, the zeroes of

straight x squared minus 2 space are space minus square root of 2 space and space square root of 2.

Now,
Sum of zeroes

equals open parentheses negative square root of 2 close parentheses plus left parenthesis square root of 2 right parenthesis space equals space 0 over 1 equals fraction numerator Coefficient space of space straight x over denominator Coefficient space of space straight x squared end fraction

Product of zeroes

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280 Views

413. Find the zeroes of a quadratic polynomial 5x² – 4 – 8x and verify the relationship between the zeroes and the coefficients.

3113 Views

414. Find the zeroes of the following polynomial and verify the relationship between the zeroes and the coefficients

5 square root of 5 straight y squared plus 20 straight y plus 3 square root of 5

90 Views

415.

Verify that 3, -1, $fraction numerator negative 1 over denominator 3 end fraction$ are the zeroes of the cubic polynomial p(x) = 3x³ – 5x² –11x – 3 then verify the relationship between the zeroes and the coefficients.

2259 Views

416. Verify that the numbers given along side of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficient in each case.
x³ – 4x² + 5x – 2, 2, 1, 1.

132 Views

417. Kind a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

270 Views