A quadratic equation has the standard form ax² + bx + c = 0 where a b and c are numbers and a is not equal to 0. We can solve it using the quadratic formula -b ± √(b² – 4ac) divided by 2a to find the x-values that make the equation true.
A quadratic equation follows the standard form ax² + bx + c = 0 where a b and c represent constant terms and a cannot be zero. Students learn to solve these equations using factorization square completion and quadratic formula methods. Solutions represent the x-values where the parabola intersects the x-axis. Real-world applications include projectile motion calculating area and analyzing profit-loss scenarios.
The chapter covers finding roots nature of roots relationship between discriminant and roots and applications in daily life. Students also learn graphical representation to visualize solutions as x-intercepts of parabolas.
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The quadratic equation whose roots are 5 and -2 is: x² – 3x – 10 = 0
Let’s verify:
If α = 5 and β = -2 are roots then:
Sum of roots = -(coefficient of x)/coefficient of x²
α + β = -b/a = 3
Product of roots = constant term/coefficient of x²
α × β = c/a = -10
Therefore x² – 3x – 10 = 0 is correct as:
– coefficient of x: -(α + β) = -3
– constant term: α × β = -10
Hence option x² – 3x – 10 = 0 is correct.
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