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Solving Using Quadratic Formula When D>0

The zeros of ...

Question

The zeros of the polynomial $x^{2} - \sqrt{2} x - 12$ are

A

(a) $\sqrt{2}, - \sqrt{2}$

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B

(b) $3 \sqrt{2}, - 2 \sqrt{2}$

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C

(c) $3 - \sqrt{2}, 2 \sqrt{2}$

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D

(d) $3 \sqrt{2}, 2 \sqrt{2}$

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Solution

The correct option is B
(b) $3 \sqrt{2}, - 2 \sqrt{2}$

$w h e n space a x squared plus b x plus c equals 0 space t h e n space x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction i n space t h e s e space q u e s t i o n x squared minus square root of 2 x minus 12 equals 0 a equals 1 comma b equals negative square root of 2 comma end root c equals negative 12 t h e n x equals fraction numerator square root of 2 plus-or-minus square root of 2 minus 4 x 1 x minus 12 end root over denominator 2 x 1 end fraction space space equals fraction numerator square root of 2 plus-or-minus square root of 2 plus 48 end root over denominator 2 end fraction space space equals fraction numerator square root of 2 plus-or-minus square root of 50 over denominator 2 end fraction space space equals fraction numerator square root of 2 plus-or-minus 5 square root of 2 over denominator 2 end fraction x equals fraction numerator square root of 2 plus 5 square root of 2 over denominator 2 end fraction space o r space fraction numerator square root of 2 minus 5 square root of 2 over denominator 2 end fraction x equals fraction numerator 6 square root of 2 over denominator 2 end fraction space o r space space fraction numerator negative 4 square root of 2 over denominator 2 end fraction x equals 3 square root of 2 space space o r space space minus 2 square root of 2 s o space o p t i o n space b space i s space c o r r e c t$

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Similar questions

Q. The zeros of the polynomial

x^{2} - \sqrt{2} x - 12

\sqrt{2}, - \sqrt{2}

3 \sqrt{2}, - 2 \sqrt{2}

- 3 \sqrt{2}, 2 \sqrt{2}

3 \sqrt{2}, 2 \sqrt{2}

Q. The zeroes of the polynomial

f (x) = x^{2} - 5 x^{2} - 2 x + 24

, if it is given that the product of its two zeroes is

12

A quadratic polynomial whose zeros are $5$ and $- 3,$ is

(a) $x^{2} + 2 x - 15$

(b) $x^{2} - 2 x + 15$

(c) $x^{2} - 2 x - 15$

(d) none of these

α

β

are the zeros of polynomial

x^{2} - 2 x - 8

then form a quadratic polynomial whose zeros are

3 α

β

The zeros of the polynomial $x^{2} - \sqrt{2} x - 12$ are _____

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