Question

Solve and explain question

Answer 1

As per the given equation we are given -

`\quad\qquad \longrightarrow\tt y = x^2 + 8x + 9 \\`

`\qquad` ★Where-

• a = 1 (Coefficient of
  `\sf x^2` )
• b = 8 (Coefficient of x)
• c = 9 (Constant term)

We are asked to find the roots of the given equation. For that, We'll find the discriminant of this equation by using the formula:-

`\quad\qquad\longrightarrow\underline{\boxed{\tt D = b²-4ac}}`

`\quad\qquad\longrightarrow\sf D = 8^(2) - 4* 1* 9`

`\quad\qquad\longrightarrow\sf D = 64-36`

`\quad\qquad\longrightarrow\sf D=28`

Since, D>0 hence, this equation will have distinct and real roots.

Formula to be applied now is as follows:-

`\quad\qquad\longrightarrow\underline{\boxed{\tt x = (-b±√D)/(2a)}}`

`\quad\qquad\longrightarrow\sf x = ( - ( 8)± √(28) )/(2* 1)\\ \\`

`\quad\qquad\longrightarrow\sf x = (\bigg[-8 ± √((4 * 7))\bigg])/( 2)`

`\quad\qquad\longrightarrow\sf x = ((-8 ± 2√7) )/( 2)`

`\quad\qquad\longrightarrow\sf x = (2(-4 ± 2√7) )/( 2)`

`\quad\qquad\longrightarrow\sf x = \frac{\cancel{2} (-4±√7)}{\cancel{2}}`

`\quad\qquad\longrightarrow\sf\boxed{\sf x = (-4 ± √7)}\\`

• Hence, the required zeros are:-

`\qquad\underline{\tt x = (-4+√7) \:and \:(-4-√7)}\\`

Answer 2

x = -4 ± √7 or x = -4 + √7 and x = -4 - √7

Explanation:

To find the roots of the quadratic equation y = x^2 + 8x + 9 using the quadratic formula, we'll use the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0.

For the given equation y = x^2 + 8x + 9, we have:

a = 1 (coefficient of x^2)

b = 8 (coefficient of x)

c = 9 (constant term)

Now, let's plug these values into the quadratic formula to find the roots:

x = (-(8) ± √(8^2 - 4 * 1 * 9)) / 2 * 1

x = (-8 ± √(64 - 36)) / 2

x = (-8 ± √28) / 2

Now, let's simplify further:

x = (-8 ± √(4 * 7)) / 2

x = (-8 ± 2√7) / 2

Now, we can factor out a 2 from the numerator:

x = 2(-4 ± √7) / 2

The 2 in the numerator and denominator cancel out:

x = -4 ± √7

So, the roots of the quadratic equation y = x^2 + 8x + 9 are:

x = -4 + √7

x = -4 - √7