Question

Find the zeroes of the following quadratic polynomial -x + 3x² - 4 and
verify the relationship Between zeroes and co-efficients.​

Answer 1

▪Given :-

A Quadratic Polynomial $\sf - x + 3 {x}^{2} - 4$

i.e $\bf 3{x}^{2} - x - 4$

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▪To Find :-

Zeros of the Given Quadratic Polynomial.

Also To Verify Relationship between Zeros And Coefficient

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▪ Relationship :-

For a Quadratic Polynomial

$\bf a {x}^{2} + bx + c$

$\sf Sum \: of \: zeros = - \frac{ b}{a} \\ \\ \sf Product \: of \: zeros = \frac{c}{a}$

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▪Solution :-

《Finding Zeros》

$3 {x}^{2} - x - 4 \\ \\ 3 {x}^{2} - 4x + 3x - 4 \\ \\ x(3x - 4) + 1(3x - 4) \\ \\ (3x - 4)(x + 1)$

So Zeros Are :

$\bf - 1 \: \: and \: \: \dfrac{4}{3}$

《 Verifying Relationship 》

$\sf Sum = - 1 + \dfrac{4}{3} \\ \\ = \bf\frac{1}{3} = - \frac{ b}{a} \: \: \: \: \: \: \: \: \: \{verified \} \\ \\ \sf Product = - 1 \times \frac{4}{3} \\ \\ \bf = - \frac{4}{3} = \frac{c}{a} \: \: \: \: \: \: \: \: \: \{verified \}$

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Answer 2

Given :-

-x + 3x - 4

To Find :-

Zeroes

Solution :-

At first we need to rearrange it

3x² - x - 4

Now, Finding zeroes by factorization method

3x² - (4x - 3x) - 4 = 0

3x² - 4x + 3x - 4 = 0

x(3x - 4) + 1(3x - 4) = 0

(3x - 4)(x + 1) = 0

So,

3x - 4 = 0

3x = 0 + 4

3x = 4

x = 4/3

Or,

x + 1 = 0

x = 0 - 1

x = -1

Sum of zeroes = -b/a

-1 + 4/3 = -(-1)/3

-3 + 4/3 = 1/3

1/3 = 1/3

Product of zeroes c/a

-1 × 4/3 = -4/3

-4/3 = -4/3