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plz answer me its related to quadratic equation ​

Answer 1

Answer:

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Examples of Quadratic Equation

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.

Standard Form Equations

Here are examples of quadratic equations in the standard form (ax² + bx + c = 0):

6x² + 11x - 35 = 0

2x² - 4x - 2 = 0

-4x² - 7x +12 = 0

20x² -15x - 10 = 0

x² -x - 3 = 0

5x² - 2x - 9 = 0

3x² + 4x + 2 = 0

-x² +6x + 18 = 0

Here are examples of quadratic equations lacking the linear coefficient or the "bx":

2x² - 64 = 0

x² - 16 = 0

9x² + 49 = 0

-2x² - 4 = 0

4x² + 81 = 0

-x² - 9 = 0

3x² - 36 = 0

6x² + 144 = 0

Here are examples of quadratic equations lacking the constant term or "c":

x² - 7x = 0

2x² + 8x = 0

-x² - 9x = 0

x² + 2x = 0

-6x² - 3x = 0

-5x² + x = 0

-12x² + 13x = 0

11x² - 27x = 0

Answer 2

Answer:

Given

$2 {x}^{2} - 7x + k$

${ \alpha }^{2} + { \beta }^{2} + \alpha \beta = \frac{67}{4}$

So

Sum of roots =

$\alpha + \beta = \frac{ - b}{a} \\ = \frac{ - ( - 7)}{2}$

$= \frac{7}{2}$

So

${ \alpha }^{2} + { \beta }^{2} + \alpha \beta \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta + \alpha \beta$

so

${ (\frac{7}{2}) }^{2} - \alpha \beta$

Now

$\alpha \beta = \frac{k}{2}$

$\frac{49}{4} - \frac{k}{2} = \frac{67}{4}$

$\frac{49 - 67}{4} = \frac{k}{2}$

$\frac{k}{2} = \frac{18}{4}$

$\frac{k}{2} = \frac{9}{2}$

$k = 9$