Find the zeroes of the quadratic polynomial x ² + 7x + 10, and verify the relati...

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itsmejeanraizerosale @itsmejeanraizerosale

October 2022 1 13 Report

Find the zeroes of the quadratic polynomial x ² + 7x + 10, and verify the relationship between the zeroes and the co-efficient

Pahelp @itzRainbowsparkle

Plss

Nonsense=Report

Answers & Comments

ItzRainbowsparkle

Given:

x²+7x + 10

To Find

Zeroes

Solution

x² + 7x + 10 = 0

Spillting middle term

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: x²+(5x+ 2x) +10 = 0 \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x²+ 5x + 2x +10 = 0 \: \: \: \: \: \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x(x +5)+ 2(x +5) = 0 \: \: \: \: \: \: \: \: \: \: \: }$

$\large{\red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ (x +5)(x+ 2) = \: 0 \: \: \: \: \: \: \: \: \: \: \: }}$

So,

Either

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x+5 = 0 \: \: \: \: \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 0 - 5 \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = -5}$

Or,

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x+2 = 0 \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 0 -2 \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x= -2 \: \: \: \: \: \: \: \: \: \: \: }$

Zeroes are -5 and -2.

$\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

VERIFICATION:

Sum of zeroes

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: a+ß -b/a \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: -5+(-2) = -(7)/1 \: \: \: \: \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -5-2 =-7/1 \: \: \: \: \: \: \: }$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -7=-7} \bold{[Verified] \: \: \: \: \: \: \: \: \: \: \: \: }$

$\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

Product of zeroes

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: aß = c/a}$

$\large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -5x-2= 10/1 \: \: }$

$\large{\red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 10 =10}}{\bold{\red{[Verified]}}}$

$\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

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