Question

PX is equal to 8 x square - 19 x minus 15 ​

Answer 1

Step-by-step explanation:

Given -

p(x) = 8x² - 19x - 15

To Find -

• Zeroes of the polynomial.
• Verify the relation between the zeroes and the coefficient of the polynomial.

Now,

8x² - 19x - 15

= 8x² - 24x + 5x - 15

(By middle term splitt)

= 8x(x - 3) + 5(x - 3)

= (8x + 5)(x - 3)

Then,

Zeroes are -

8x + 5 = 0 and x - 3 = 0

• x = - 5/8 and x = 3

Let α = 3 and β = -5/8

Verification -

α + β = -b/a

= 3 + (-5/8) = -(-19)/8

= 3 - 5/8 = 19/8

= 24 - 5/8 = 19/8

= 19/8 = 19/8

LHS = RHS

And

αβ = c/a

= 3 × -5/8 = -15/8

= -15/8 = -15/8

LHS = RHS

Hence,

Verified..

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ x = 3

$\implies$ x = -5/8

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

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

• p(x) = 8x² - 19x - 15

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

• zero of the polynomial
• verify relation between the zeroes and the coefficient of the polynomial.

$\large\underline\mathrm{Solution}$

$\implies$ 8x² - 19x - 15 = 0

$\implies$ 8x² - 24x + 5x - 15 = 0

$\implies$ 8x(x - 3) + 5(x - 3)

$\implies$ (8x + 5)(x - 3)

$\large\underline\mathrm{then}$

$\implies$ 8x + 5 = 0

$\implies$ x = -5/8

$\implies$ x - 3 = 0

$\implies$ x = 3

Let α = 3 and β = -5/8

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

$\implies$ α + β = -b/a

$\implies$ 3 + (-5/8) = -(-19)/8

$\implies$ 3 - 5/8 = 19/8

$\implies$ 24 - 5/8 = 19/8

$\implies$ 19/8 = 19/8

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

$\large\underline\mathrm{And}$

$\implies$ αβ = c/a

$\implies$ 3 × -5/8 = -15/8

$\implies$ -15/8 = -15/8

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

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

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

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