Question

27. A quadratic polynomial, whose zeroes are -2 and 5 can be(1) x^{2}-3x-10 (2) x^{2}+3x-10 (3) x^{2}+3x+10 (4) x^{2}-3x+10 `​

Answer 1

Answer:

x² - 3x - 10

Step-by-step explanation:

Let the zeroes of quadratic equation be α and β respectively. Here α is -2 and β is 5.

General form of quadratic equation:

x² - (Sum of zeroes)x + Product of zeroes

= x² - (α + β)x + αβ

Now putting the value of α and β in the general form.

x² - (α + β)x + αβ

= x² - (-2 + 5)x + (-2 × 5)

= x² - 3x + (-10)

= x² - 3x - 10

So OPTION [1] is correct. ✔️

Let's learn something more about quadratic equation.

1. The general form of quadratic equation is ax² + bx + c

2. Maximum number of roots of quadratic equation is two.

3. The roots of quadratic equation can be found by the formula -b ± √b² - 4ac/2a. It is known as Sridharacharya* Formula or Quadratic Equation Formula.

4. The nature of roots is decided by discriminant of quadratic equation which is given by b² - 4ac

5. If b² - 4ac > 0 then roots are distinct and real; if b² - 4ac < 0 then distinct and imaginary; if b² - 4ac = 0 then both the roots are equal and real.

*Sridharacharya was a great ancient mathematician.