Question

find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 3x^2-x-4. find alpha + Beeta and Alpha×beeta. -b by a and c by a . please find it​

Answer 1

Step-by-step explanation:

3x²-x-4=0------(1)

3x²-4x+3x-4=0

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

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

x=4/3 ,-1

Now

from eq 1 we get

a=3

b=-1

c=-4

α+β= -b/a = -(- 1)/3=1/3

αβ=c/a= -4/3

Relationship

x²-(α+β)x+(αβ)

x²-(1/3)x+(-4/3)

3x²-x-4=0

I think it is helpful for you

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \huge\colorbox{yellow}{ ❛Answer❜} \\ \\ \\ \\ {\underline{\sf{\pink{∴ \: 3 {x}^{2} - x - 4 = 0}}}} \\ {\sf{∴ \: a {x}^{2} + bx + c = 0}} \\ {\sf{\blue{∴ \: a = 3, \: b = - 1, \: c = - 4}}} \\ \\ {\sf{\purple{∴ \: 3 {x}^{2} - 4x + 3x - 4 = 0 }}} \\ {\sf{→ \: x(3x - 4) + 1(3x - 4) = 0}} \\ {\sf{→ \: (3x - 4)(x + 1) = 0}} \\ {\boxed{\underline{\underline{\bf{\orange{∴ \: x = \frac{4}{3} }}}}}} \: \: \: {\sf{or}} \: \: \: {\boxed{\underline{\underline{\bf{\orange{∴ \: x = - 1 }}}}}} \\ \\ \\ \\ \\ \\ {\underline{\sf{\green{Verification \: ✓}}}} \\ \\ {\boxed{\sf{\orange{sum \: of \: zeroes = \frac{ - b}{a} = \frac{ - ( - 1)}{3} = \frac{1}{3} }}}} \\ \\ {\boxed{\sf{\orange{product \: of \:zeroes = \frac{c}{a} = \frac{ - 4}{3} }}}}$

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