Question

Find the Zeroes of Polynomials below and make Relationship with Zeroes and Coefficients.
(i) P(X) = 2x² + X - 6
(ii) P(X) = 3x² -5x +2
(iii) P(X) = 3x²-x + 2
(iv) P(X) = 2x² + 45x -47
(v) P(X) = 2x² + 5x -3
(vi) P(X) = x² - 5x + 6
PLS Answer these, I will Mark as Brainliest.​

Answer 1

Answer:

(i) P(X) = 2x² + X - 6

= 2$x^2$ – 4$x$ + 3$x$ – 6 = 0

= 2$x$ ($x$-2) + 3 ($x$-2) = 0

= (2$x$ + 3) = 0    

= ($x$ – 2) = 0

= ∝ = -3/2 and β = 2

= ∝ + β = -3 x 2 = -6 = c/a

= a$x^2$ + b$x$ + c = 0

= 2$x^2$ – $x$ – 6 = 0

= ∝ + β = ½ - 2/3 = -1/6

(ii) P (x) = 3x2-5x+2

Sol: = 3$x^2$ = 3$x$ – 2$x$ + 2

= 3$x$ ($x$-1) -2 ($x$-1)

= ($x$-1) (3$x$-2) = 0

= ($x$-1) = 0      

= $x$ = 1

= 3$x$ -2 = 0

= 3$x$ – 2 = 0

= 3$x$ = 2

= $x$ = 2/3

=> Sum of Zeroes  

= 1/3 + 2/3 = 3 + 2/3 = 5/3

=> Product of Zeroes  

= 1 x 2/3 = 2/3

= a = 3, b = -5, c = 2

= ∝ + β = -b/a

= ∝ + β = -b/a

= ∝ + β = -(-5)/3 = 5/3

= ∝β = c/a = 2/3

(iii) P (x) = 3x2 – x + 2

Sol: = 3$x^2$ – 3$x$ + 2$x$ -2

= 3$x$ ($x$-1) (3$x$ + 2) = 0

= ($x$ - 1) (3$x$ + 2) = 0

= ($x$ - 1) = 0

= $x$ = 1

= (3$x$+2) = 0

= (3$x$) = -2/3

=> Sum of Zeroes  

= $x$ = 1

= $x$ = -2/3

= ∝ + β = 1 – 2/3

= 3-2/3 = 1/3

= ∝β = 1/3

= ∝β = (1) (-2)

= -2/3

(iv) P (x) = 2x2 + 45x – 47

= 2$x^2$ + 45$x$ – 47 = 0

= 2$x^2$ + 47$x$ – 2$x$ – 47 = 0

= $x$ (2$x$+47) – 1 (2$x$ + 47) = 0

= ($x$ - 1) = 0

= $x$ = 1

= (2$x$+ 47) = 0

= 2$x$ = -47  

= $x$ = -57/2

∴ ∝ = 1,  β = -47/2

=> Sum of Zeroes = (1) (-47/2)

= 1 -47/2 = 46/2

= Product of Zeroes = (1) (-47/2)

= p(x) = 2x2 + 45x – 47

= a$x^2$ + b$x$ - c

= a = 2, b = 45, c = -47

= ∝ + β = -b/a

= -45/2 = 22.5

= ∝β = c/a

= (1) (-45) = -47/2 =- 23.5

(v) P(X) = 2x² + 5x -3

= 2$x^2$ + 6$x$ - $x$ - 3

= 2$x$ ($x$+3) -1 ($x$+3)

= (2$x$-1) = 0

= 2$x$ = 1

= $x$ = 1/2

= ($x$+3) = 0

= ($x$ = -3)

= $x$ = 1/2

∴ ∝ = 1/2, β = -3

= ∝ + β = -b/a

= 1/2 + (-3) = -5/2

= -6 + 1/2 = -5/2

= -5/2

= ∝β = c/a

= 1/2 x -3 = -3/2

= -3/2

(vi) P(X) = x² - 5x + 6

= $x^2$ - 5x + 6

= $x^2$ + $x$ - $6x$ + 6

= $x$ ($x$ + 1) -6 ($x$ + 1)

= ($x$ - 6) = 0

= $x$ = 6

= ($x$ + 1) = 0

= ($x$ = -1)

=> Sum of Zeroes = a + b = -b/a

= 6 - 1 = - (-5)/1

= (5 = 5)

=> Product of Zeroes = ab = c/a

= (6) (-1) = 6

= (6 = 6)

==>HOPE YOU UNDERSTOOD THIS!