Question

Find the zeroes of quadratic polynomial and verify the relationship between the zeroes and the coefficients - 3x2+7x+4=0

Answer 1

Given :-

• Equation is 3x² + 7x + 4 = 0

To Find :-

• zeroes of quadratic polynomial and verify the relationship between the zeroes and the coefficients . ?

Solution :-

Solving The Equation by Splitting The Middle Term :-

→ 3x² + 7x + 4 = 0

→ 3x² + 3x + 4x + 4 = 0

→ 3x(x + 1) + 4(x + 1) = 0

→ (3x +4)(x + 1) = 0

Putting both Equal to Zero now, we get,

→ (3x + 4) = 0

→ 3x = (-4)

→ x = (-4/3).

Or,

→ (x + 1) = 0

→ x = (-1).

________________________

Now, First Relation is :-

→ Sum of Zeros = - (coefficient of x) /(coefficient of x²)

Putting both values ,

→ (-1) + (-4/3)) = -(7)/3

→ (-7/3) = (-7/3) ✪✪ Hence Verified. ✪✪

Second Relation :-

→ Product Of Zeros = Constant Term / (coefficient of x²)

Putting both Values ,

→ (-1) * (-4/3)) = 4 / (3)

→ 4/3 = 4/3 ✪✪ Hence Verified. ✪✪

______________________________

Answer 2

Question:

Find the zeroes of quadratic polynomial and verify the relationship between the zeroes and the coefficients

$3 {x}^{2} + 7x + 4$

Answer:

$given \\ 3 {x}^{2} + 7x + 4 \\ \\ \implies 3 {x}^{2} + 3x + 4x + 4 \\ \\ \implies3x(x + 1) + 4(x + 1) \\ \\ \implies \: (3x + 4)( x+ 1)\\ \\ take \: \\ \\ 3x + 4 = 0 \: \: \: \: x + 1 = 0 \\ \\ 3x = - 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 1 \\ \\ x = \frac{ - 4}{3} \: \: \: \: \: \: \: \: x = - 1$

Hence the value of X= -4/3 and -1

$sum \: of \: zeroes \: = \frac{ - 4}{3} + ( - 1) = \frac{ - 7}{3} = - \frac{coff. \: of \: x}{coff. \: of \: {x}^{2} } \\ \\ product \: of \: zeros = - \frac{ - 4}{3} \times (- 1) = \frac{4}{3} = \frac{contant \: term}{coff \: of \: {x}^{2} }$