Question

find the zeros of quadratic polynomial 3 x square - 4 x minus 7 and also verify the relationship between zeroes and its coefficients​

Answer 1

Answer:

WE ARE GIVEN A QUADRATIC POLYNOMIAL:

⇒3x²-4x-7=0

It is in the form ax²+bx+c=0

Here, a=3; b= -4; c= -7.

Factorise it.

⇒3x²-7x+3x-7=0

⇒x(3x-7)+1(3x-7)=0

⇒(3x-7)(x+1)=0

Now, equate it to 0.

x= -1 OR x= 7/3

Now, here:

Sum of roots = -b/a

-1+7/3= -(-4/3)

4/3=4/3.

Product of roots = c/a

-1×7/3 = -7/3

-7/3=-7/3.

${\huge{\mathfrak{\underbrace{\blue{HOPE \:\: THIS \:\: HELPS \:\: :D}}}$

Answer 2

Answer:

Given Quadratic polynomial

Factorisation :

$3 {x}^{2} - 4x - 7 = 0 \\ 3 {x}^{2} - 7x + 3x - 7 = 0 \\ x(3x - 7) + 1(3x - 7) = 0 \\ (3x - 7)(x + 1) = 0 \\ 3x - 7 = 0 \: \: or \: \: x + 1 = 0 \\ x = \frac{7}{3} \: \: or \: \: x = - 1 \\ \alpha= - 1 \: \: and \: \: \beta= \frac{7}{3}$

$sum \: of \: the \: zeroes \: \\ \alpha + \beta = - 1 + \frac{7}{3} \\ \alpha + \beta = \frac{4}{3} \\ \\ product \: of \: zeroes \\ \alpha \beta = ( - 1)( \frac{7}{3}) \\ \alpha \beta = - \frac{7}{3}$

$coefficients \\ a = 3 \: \: \: b = - 4 \: \: \: c = - 7 \\ zeroes \\ \alpha = - 1 \: \: \: \beta = \frac{7}{3} \\ \\ \alpha + \beta = - \frac{b}{a} = \frac{4}{3} \\ \alpha \beta = \frac{c}{a} = - \frac{7}{3}$

Hence verified