Question

find the zeros of quadratic polynomial 3 x square minus x minus 4 and verify the relationship between the zeros and its coefficient ( plz ans stp by stp and solve it in a paper)

Answer 1

$\huge{ \bold \: { \: Solution }}$




$equation =$
$\underline{\bold{3 {x}^{2} - x - 4 = 0}}$



Now we factorise this equation-----

$3 {x}^{2} - 4x + 3x - 4 = 0 \\ \\ x(3x - 4) + 1(3x - 4) = 0 \\ \\ (3x - 4)(x + 1) = 0 \\ \\ 3x - 4 = 0 \: \: \: \: \bold{or} \: \: x + 1 = 0 \\ \\ \bold{x = \frac{4}{3} \: \: \: or \: \: \: x = - 1}$
$\\ \\ \: \bold{ \alpha = \frac{4}{ 3} \: \: \: \: or \: \: \: \beta = - 1}$
$equation = 3 {x}^{2} - x - 4 \\ \\ here..... \\ a = 3 \: \\ b = - 1 \\ c = - 4$

Now , Verification of Zeroes of polynomial and Coefficient of polynomial.

$\huge{ \bold{ \underline{ \pink{ \: STEP - I }}}}$

$\bold{ \alpha + \beta = \frac{ - b}{a} } \\ \\ \frac{4}{3} +( - 1) = \frac{ - ( - 1)}{3} \\ \\ \frac{4}{3} - 1 = \frac{1}{3} \\ \\ \frac{4 - 3}{3} = \frac{1}{3} \\ \\ \frac{1}{3} = \frac{1}{3}$

$\huge{ \underline{ \bold{ \pink{ \: \: STEP-II \: \: \: }}}}$

${\bold{ \alpha \times \beta = \frac{c}{a} }}$
$\\ \frac{4}{3} \times - 1 = \frac{ - 4}{3} \\ \\ \frac{ - 4}{3} = \frac{ - 4}{3}$

Here , LHS = RHS

$\huge{ \underline{ \bold{ \red{ \: \: \: \: \: Hence, Verified \: \: \: \: \: \: }}}}$

Answer 2

Step-by-step explanation:

3x2 - x - 4

3x2 + 3x - 4x -4 = 0

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

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

x + 1 = 0

x = -1

3x - 4 = 0

x = 4/3

Hope this answer help u