I need help with these questions ( see image for question ).Please show working.

Mathematics

1 answer:

antiseptic1488 [7]2 years ago

5 0

Answer:

k = -4 ± 2√5

Step-by-step explanation:

#22

<h3>Given </h3>

Equation x² -4x + 1 = k(x - 4) with equal roots

The value of k

<h3>Solution</h3>

<u>The equation in standard form is:</u>

x² -4x + 1 = k(x - 4)
x² - 4x - kx + 1 + 4 = 0
x² - (k + 4)x + 5 = 0

<u>When the quadratic equation has equal roots its discriminant is zero</u>

D = 0
b² - 4ac = 0
(k + 4)² - 4*5 = 0
(k + 4)² = 20
k + 4 = ± √20
k = - 4 ± √20
or
k = -4 ± 2√5

You might be interested in

Vector u has its initial point at (-7,2) and it's terminal point at (11,-5). Vector v has a direction opposite that of vector u,

PSYCHO15rus [73]

Answer:

$3\vec{v} = ( - 21,54)$

Step-by-step explanation:

$\vec{u} = (18,- 7)\Rightarrow \vec{v} = ( - 7,18) \Rightarrow 3\vec{v} = ( - 21,54)$

8 0

2 years ago

4.8/1 7/9 =(1.2b):6 2/3

Hunter-Best [27]

Answer:

b = 15

Step-by-step explanation:

Solve for b:

$\dfrac{4.8}{1\frac{7}{9}}=\dfrac{1.2b}{6\frac{2}{3}}$

Cross multiply:

$6\dfrac{2}{3}\cdot 4.8=1.2b\cdot 1\dfrac{7}{9}\\ \\\dfrac{6\cdot 3+2}{3}\cdot 4.8=1.2b\cdot \dfrac{9+7}{9}\\ \\\dfrac{20}{3}\cdot \dfrac{48}{10}=\dfrac{12b}{10}\cdot \dfrac{16}{9}\\ \\20\cdot 4=b\cdot \dfrac{16}{3}\\ \\5=b\cdot \dfrac{1}{3}\\ \\b=5\cdot 3\\ \\b=15$