What kind of roots or solution each of the quadratic equation?
b. Write the quadratic equation that has two distinct or real unequal roots.
c. Write the quadratic equation that has two real equal roots.
d. Write the quadratic equation that has no real roots.
e. Write quadratic equation that has irrational roots.
Answers
Given : x² + 4x - 12 = 0
2x² + 6x - 108 = 0
3x² - 3x - 270 =0
x² - 11x + 10 = 0
x² - 4x + 24 = 0
x² + 16x + 64 =0
To Find : What kind of roots or solution each of the quadratic equation?
b. Write the quadratic equation that has two distinct or real unequal roots.
c. Write the quadratic equation that has two real equal roots.
d. Write the quadratic equation that has no real roots.
e. Write quadratic equation that has irrational roots.
Solution:
ax² + bx + c = 0
D = b² - 4ac
D > 0 roots real and unequal
D = 0 Roots equal and real
D < 0 no real roots
D > 0 and not a perfect square - irrational roots
x² + 4x - 12 = 0
D = 4² - 4(1)(-12) = 64 = 8²
quadratic equation has two distinct or real unequal roots.
-6 , 2
2x² + 6x - 108 = 0
=> x² + 3x - 54 = 0
D = 3² - 4(1)(-54) = 225 = 15²
quadratic equation has two distinct or real unequal roots.
-9 , 6
3x² - 3x - 270 =0
=> x² - x - 90 = 0
D = 361 = 19²
quadratic equation has two distinct or real unequal roots.
10 , -9
x² - 11x + 10 = 0
=> D = 81 = 9²
quadratic equation has two distinct or real unequal roots.
10 , 1
x² - 4x + 24 = 0
D = -80 <
quadratic equation has no real roots.
x² + 16x + 64 =0
=> D = 0
quadratic equation that has real equal roots.
-8 , - 8
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