Question

(vi) 3x2 - x - 4 find the zero and coefficient of the polynominal​

Answer 1

Given :-

• Equation :- 3x² - x - 4$.$

Have to Find :-

• Find the zero and coefficient of the polynomial.

Solution :-

By using middle term splitting method.

⇒ 3x² - ( 4 - 3 ) x - 4

⇒ 3x² - 4x + 3x - 4

Taking common :-

⇒ x ( 3x - 4 ) + 1 ( 3x - 4 )

⇒ ( 3x - 4 ) ( x + 1 )

Putting it equal zero.

★ 3x - 4 = 0

↬ 3x = 4

↬ x = 4/3

★ ( x + 1 ) = 0

↬ x = ( -1 )

Required Zeroes are :- 3/4 and ( -1 )

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Coefficient of the polynomial

Leading coefficient with highest degree 2 is 3

Answer 2

Answer:

$\huge\rm{Solution:-} \\ \rm→ax²+bx+c \\ \rm→a=3; \: b=-1; \: c=-4 \\ \rm \: Sum \: of \: coefficient= \frac{-b}{a} = \frac{-(-1)}{3} = \frac{1}{3} \\ \rm \: Product= \frac{c}{a} = \frac{-4}{3}$

$\rm→3x²-x-4 \\ \rm→3x²+3x-4x-4 \\ \rm→3x(x+1)-4(x+1) \\ \rm→(x+1)(3x-4) \\ \rm→x=-1 \: \: \: \: \: \: \: \: \: x= \frac{4}{3} \\ \rm \: Sum \: of \: zeroes= \frac{-1}{1} + \frac{4}{3} = \frac{-3+4}{3} = \frac{1}{3} \\ \rm \: Product \: of \: zeroes=(-1) (\frac{4}{3}) = \frac{-4}{3}$

The relationship between zeroes and co-efficients verified and the values are matching