Question

1. Find the zeros of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
6x^2-3-7x

Answer 1

Step-by-step explanation:

Given -

Quadratic polynomial is 6x² - 7x - 3

To Find -

• Zeroes of the polynomial
• Verify the relationship between the zeroes and the coefficient

Now,

6x² - 7x - 3 = 0

» 6x² - 9x + 2x - 3

» 3x(2x - 3) + 1(2x - 3)

» (3x + 1)(2x - 3)

Zeroes are -

3x + 1 = 0 and 2x - 3 = 0

• x = -1/3 and x = 3/2

Verification -

Let α = -1/3 and β = 3/2

In polynomial 6x² - 7x - 3 = 0

here,

a = 6

b = -7

c = -3

Now,

α + β = -b/a

» -1/3 + 3/2 = -(-7)/6

» -2+9/6 = 7/6

» 7/6 = 7/6

LHS = RHS

and

αβ = c/a

» -1/3 × 3/2 = -3/6

» -3/6 = -3/6

» -1/2 = -1/2

LHS = RHS

Hence,

Verified..

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ x = -1/3

$\implies$ x = 3/2

$\large\underline\mathrm{the \: equation \: is \: verified.}$

$\large\underline\mathrm{Given:-}$

• Quadratic polynomial is 6x² - 7x - 3

$\large\underline\mathrm{To \: find}$

• zeroes of the polynomial.
• verify the relationship between the zeroes of the coefficient.

$\large\underline\mathrm{Solution}$

$\implies$ 6x² - 7x - 3 = 0

$\implies$ 6x² - 9x + 2x - 3 = 0

$\implies$ 3x(2x - 3) + 1(2x - 3) = 0

$\implies$ (3x + 1)(2x - 3)

$\implies$ 3x + 1 = 0

$\implies$ x = -1/3

$\implies$ 2x - 3 = 0

$\implies$ x = 3/2

$\large\underline\mathrm{verification:-}$

Let α = -1/3 and β = 3/2

• In polynomial 6x² - 7x - 3

$\implies$ a = 6

$\implies$ b = -7

$\implies$ c = -3

$\large\underline\mathrm{Now,}$

$\implies$ α + β = -b/a

$\implies$ -1/3 + 3/2 = -(-7)/6

$\implies$ -2 + 9/6 = 7/6

$\implies$ 7/6 = 7/6

LHS = RHS

$\large\underline\mathrm{And,}$

$\implies$ αβ = c/a

$\implies$ -1/3 × 3/2 = -3/6

$\implies$ -3/6 = -3/6

$\large\underline\mathrm{LHS \: = \: RHS}$

$\large\underline\mathrm{Hence,}$

$\large\underline\mathrm{the \: equation \: is \: verified.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$