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Find the zeros of 3 x …

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Find the zeros of 3 x square minus x minus 4 and verify the relationship between zeroes and its coefficient

Posted by Thejasprasad Bk 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

We have,f(x) = 3x² - x - 4

= 3x²- 4x + 3x - 4
= x(3x - 4) + 1(3x - 4)
= (3x - 4) )(x + 1)
{tex}\therefore{/tex} f(x) = 0
{tex}\Rightarrow{/tex} (3x - 4)(x +1) = 0
{tex}\Rightarrow{/tex} 3x - 4 = 0 or x + 1 = 0
{tex}\Rightarrow x = \frac { 4 } { 3 }{/tex} or x = -1
So, the zeros of f(x) are {tex}\frac { 4 } { 3 } \text { and } - 1{/tex}

Now sum of zeros {tex}= \frac { 4 } { 3 } + ( - 1 ) = \frac { 1 } { 3 } = \frac { - ( \text { coefficient of } x ) } { \left( \text { coefficient of } x ^ { 2 } \right) }{/tex}.
And product of zeros {tex}= \frac { 4 } { 3 } \times ( - 1 ) = \frac { - 4 } { 3 } = \frac { \text { constant term } } { \left( \text { coefficient of } x ^ { 2 } \right) }{/tex}

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If 1/2 is a root of equation x^2+kx- 5/4 =0 , then what is the value of k

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CBSE > Class 10 > Mathematics