Mathematics, 29.11.2020 18:30 harleyquinn1241

Hi. Please help me with these questions
See image for question. Answer no 6 and 7

Hi. Please help me with these questions
See image for question.Answer no 6 and 7

Answers: 3

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Answers

Answer from: jinxjungkook3

6. See solution7. k = 2, k = -6

Step-by-step explanation:

Given equation:

2(x + 2)² + p(x + 1) = 0The sum of the roots is q1 and the product of the roots is q2

Need to show that q1+q2 = 0

Solution

Bringing the equation into standard form of ax² + bx + c = 0:

2(x + 2)² + p(x + 1) = 0 2x² + 8x + 8 + px + p = 02x² + (p + 8)x + (p + 8) = 0

Sum of the roots:

q1 = - b/a = -(p + 8)/2

Product of the roots:

q2 = c/a = (p + 8)/2

We see that q1 and q2 are opposite numbers, therefore their sum equals zero:

q1 + q2 = -(p + 8)/2 + (p + 8)/2 = 0

Given quadratic equation:

x² - (k + 2)x + 4 = 0It has equal roots

Need to find the possible values of k

Solution

When the quadratic equation has equal roots, then its discriminant is equal to zero:

D = 0√b² - 4ac = 0√(-k -2)² - 4*1*4 = 0√k² + 4k + 4 - 16 = 0√k² + 4k - 12 = 0k² + 4k - 12 = 0k = {-4 ± √4² -4*1*(-12)}/2 k = (-4 ± √16 + 48)/2k = (-4±√64)/2k = -2 ± 4k = 2, k = -6

Answer from: Quest

Aperecent is the answer

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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Hi. Please help me with these questions
See image for question. Answer no 6 and 7