sum of zeros of the polynomial p(x²)=x²-kx+9+is7.find the value of k
Answers
EXPLANATION.
Sum of zeroes of the polynomial.
⇒ p(x) = x² - kx + 9 is 7.
As we know that,
Put the value of x = 7 in equation, we get.
⇒ p(7) = (7)² - k(7) + 9.
⇒ 49 - 7k + 9 = 0.
⇒ 58 - 7k = 0.
⇒ 7k = 58.
⇒ k = 58/7.
MORE INFORMATION.
Nature of the zeroes of the quadratic expression.
(1) = Real and different, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Given that: Sum of zeros of the polynomial is p(x) = x²-kx+9=7
To find: The value of k
Solution: The value of k = 58/7
Procedure: To solve this question we have to put 7 at the place of x then we just have to solve it as that it. It is very easy to solve. Let us see how to solve!
Full Solution:
➼ p(x) = x²-kx+9=7
➼ p(7) = 7² - k(7) + 9
➼ 7 × 7 - k(7) + 9 = 0
➼ 49 - k(7) + 9 = 0
➼ 49 + 9 -7k = 0
➼ 58 - 7k = 0
➼ 7k = 58
➼ k = 58/7
Henceforth, the value of k is 58/7
Some knowledge about Quadratic Equations -
★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a
★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a
★ Discriminant is given by b²-4ac
- Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.
★ A quadratic equation have 2 roots
★ ax² + bx + c = 0 is the general form of quadratic equation
★ D > 0 then roots are real and distinct.
★ D = 0 then roots are real and equal.
★ D < 0 then roots are imaginary.
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━