write the quadratic equation that has two distinct or real unequal roots
Answers
Answer:
quadratic equation, ax2 + bx + c = 0; a ≠ 0 will have two distinct real roots if its discriminant, D = b2 - 4ac > 0. Hence, the equation x2 –3x + 4 = 0 has no real roots. Hence, the equation 2x2 + x – 1 = 0 has two distinct real roots. Hence, the equation 3x2 – 4x + 1 = 0 has two distinct real roots
Step-by-step explanation:
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The quadratic equation that has two distinct or real unequal roots
x² + 4x - 12 = 0
2x² + 6x - 108 = 0
3x² - 3x - 270 = 0
x² - 11x + 10 = 0
Given : ( Correction in the question )
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 : The quadratic equation that has two distinct or real unequal roots
Tip : General form of a quadratic equation is
ax² + bx + c = 0
The Discriminant of the quadratic equation is denoted by D and defined as
D = b² - 4ac
Case : I When D > 0 The roots real and unequal
Case : II When D = 0 The Roots equal and real
Case : III When D < 0 The equation has no real roots
Case : IV When D > 0 and not a perfect square then the roots are irrational
Solution :
1. Here the given equation is
x² + 4x - 12 = 0
D
D = 3² - 4 × 1 × (-54)
= 9 + 216
= 225
= 15²
Which is a perfect square
The equation has two distinct real unequal roots.
3. Here the given equation is
3x² - 3x - 270 =0
Which can be rewritten as x² - x - 90 = 0
D
= (-1)² - 4 × 1 × (-90)
= 1 + 360
= 361
= 19²
The equation has two distinct real unequal roots.
4. Here the given equation is
x² - 11x + 10 = 0
D
= (-11)² - 4 × 1 × 10
= 121 - 40
= 81
= 9²
The equation has two distinct real unequal roots.
5. Here the given equation is
x² - 4x + 24 = 0
D
= ( - 4)² - 4 × 1 × 24
= 16 - 96
= - 80 < 0
The equation has no real roots.
6. Here the given equation is
x² + 16x + 64 =0
D
= 16² - 4 × 1 × 64
= 256 - 256
= 0
The equation has real equal roots.
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