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Discriminant and nature of the roots
Discriminant: (43)
Nature of the roots: (44)
We will use the formula in order to find the discriminant.
The general form of a quadratic equation is ax² + bx + c = 0, therefore
∴ The discriminant is 16.
Discriminant: (45)
Nature of the roots: (46)
∴ The discriminant is -11.
Sum: (47)
Product: (48)
Sum and product of the roots
Formula for finding the sum of the roots:
Formula for finding the product of the roots:
Sum of the roots
∴ The sum of the roots is 8.
Product of the roots
∴ The product of the roots is 7.
We will use the formula in order to find the roots.
Roots: (49)
(50)
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discriminant: 16
nature of the roots: real, rational, unequal
discriminant: -11
nature of the roots: not real
sum: 8
product: 7
roots: 7, 1
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DISCRIMINANT | NATURE OF THE ROOTS | SUM AND PRODUCT OF THE ROOTS | ROOTS
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Discriminant and nature of the roots
Discriminant: (43)![\large\tt{\underline{16}} \large\tt{\underline{16}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7B16%7D%7D)
Nature of the roots: (44)![\large\tt{\underline{Real, Rational, Unequal}} \large\tt{\underline{Real, Rational, Unequal}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7BReal%2C%20Rational%2C%20Unequal%7D%7D)
We will use the formula
in order to find the discriminant.
The general form of a quadratic equation is ax² + bx + c = 0, therefore
∴ The discriminant is 16.
Discriminant: (45)![\large\tt{\underline{-11}} \large\tt{\underline{-11}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7B-11%7D%7D)
Nature of the roots: (46)![\large\tt{\underline{Not\:Real\:or\: Imaginary}} \large\tt{\underline{Not\:Real\:or\: Imaginary}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7BNot%5C%3AReal%5C%3Aor%5C%3A%20Imaginary%7D%7D)
We will use the formula
in order to find the discriminant.
The general form of a quadratic equation is ax² + bx + c = 0, therefore
∴ The discriminant is -11.
Sum: (47)![\large\tt{\underline{8}} \large\tt{\underline{8}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7B8%7D%7D)
Product: (48)![\large\tt{\underline{7}} \large\tt{\underline{7}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7B%5Cunderline%7B7%7D%7D)
Sum and product of the roots
Formula for finding the sum of the roots:
Formula for finding the product of the roots:
The general form of a quadratic equation is ax² + bx + c = 0, therefore
Sum of the roots
∴ The sum of the roots is 8.
Product of the roots
∴ The product of the roots is 7.
ROOTS
We will use the formula
in order to find the roots.
Roots: (49)![\large\tt{x_1 = \red{7}} \large\tt{x_1 = \red{7}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7Bx_1%20%3D%20%5Cred%7B7%7D%7D)
(50)![\large\tt{x_2 =\red{1}} \large\tt{x_2 =\red{1}}](https://tex.z-dn.net/?f=%5Clarge%5Ctt%7Bx_2%20%3D%5Cred%7B1%7D%7D)
I hope you find my answer helpful! Just message me directly if you don't understand my answer. Have a great day ahead!
Kindly swipe your screen to the left to see the continuation of my answer.
#CarryOnLearning
43-44
discriminant: 16
nature of the roots: real, rational, unequal
45-46
discriminant: -11
nature of the roots: not real
47-48
sum: 8
product: 7
49-50
roots: 7, 1