Math, asked by shahnarbaaz, 6 hours ago

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

Answers

Answered by SparklingBoy
96

▪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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Answered by Itzheartcracer
31

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

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