The three zeroes of the polynomial 2 x3-5 x2-28 x-15

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Standard X

Mathematics

Degree of a Polynomial

The three zer...

Question

The three zeroes of the polynomial 2x³ + 5x² - 28x - 15 _____

Are all Integers

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Are all rational numbers

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Are all Natural numbers

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All three are not real numbers

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Solution

The correct option is B
Are all rational numbers

One zero of this polynomial , by the method of Hit and Trial is 3 .Now, by long division of 2x³ + 5x² - 28x - 15 by (x -3 ) , we have 2x² + 11x + 5 factors of which are ( 2x + 1 ) and (x + 5 ).

Therefore, the three zeros of the polynomial 2x³ + 5x² - 28x - 15 are all rational numbers

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Similar questions

Q. Determine whether (x-5) is a factor of the polynomial

p (x) = 2 x^{3} - 5 x^{2} - 28 x + 15

If the zeros of the polynomial 2x³-5x²+37x-30,are in AP

If $2$ and $0$ are the zeroes of the polynomial $f (x) = 2 x^{3} - 5 x^{2} + a x + b$ then find the values of $a$ and $b$ .

Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^{3} - 2 x^{2} - 9 x + 18$ Hence factories the expression
(ii) (x+5) is a factor of $2 x^{3} + 5 x^{2} - 28 x - 15$ Hence factorise fthe expression $2 x^{3} + 5 x^{2} - 28 x - 18$ completely.
(iii) (3x+2) is a factor fo $3 x^{3} + 2 x^{2} - 3 x - 2.$ Hence factorise the expression
$3 x^{3} + 2 x^{2} - 3 x - 2$ completely

Q. Given that

x - \sqrt{5}

is a factor of polynomial

x^{3} - 3 \sqrt{5} x^{2} - 5 x + 15 \sqrt{5}

, find all zeroes of the polynomial.

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The three zeroes of the polynomial 2x3 + 5x2 - 28x - 15 _____

The three zeroes of the polynomial 2x³ + 5x² - 28x - 15 _____