рдорд░рд╛рдареА

If ЁЭЫ╝ and ЁЭЫ╜ be the zeroes of the polynomial 2тБвЁЭСе2 тИТ7тБвЁЭСе +ЁЭСШ write the value of (ЁЭЫ╝ + ЁЭЫ╜ + ЁЭЫ╝ЁЭЫ╜).

Advertisements
Advertisements

рдкреНрд░рд╢реНрди

If ЁЭЫ╝ and ЁЭЫ╜ be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (ЁЭЫ╝ + ЁЭЫ╜ + ЁЭЫ╝ЁЭЫ╜).

рдмреЗрд░реАрдЬ
Advertisements

рдЙрддреНрддрд░

By using the relationship between the zeroes of the quadratic polynomial.
We have  

Sum of zeroes = `(-("Coefficient of x"))/("Coefficient of "x^2)` 

Product of zeroes =`("Constant term")/("Coefficient of "x^2)` 

a = 2, b = −7, and c = k

∴ ∝+ β = `(-b)/c`

= `(-(-7))/2`

= `7/2`

∝β = `c/a`

= `k/2` 

Now, ЁЭЫ╝ + ЁЭЫ╜ + ЁЭЫ╝ЁЭЫ╜ = `7/2 + k/2`

= `(7 + k)/2`

shaalaa.com
  рдпрд╛ рдкреНрд░рд╢реНрдирд╛рдд рдХрд┐рдВрд╡рд╛ рдЙрддреНрддрд░рд╛рдд рдХрд╛рд╣реА рддреНрд░реБрдЯреА рдЖрд╣реЗ рдХрд╛?

рд╡реНрд╣рд┐рдбрд┐рдУ рдЯреНрдпреВрдЯреЛрд░рд┐рдпрд▓VIEW ALL [5]

рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).


The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).


Find all the zeroes of `(2x^4 – 3x^3 – 5x2 + 9x – 3)`, it is being given that two of its zeroes are `sqrt3 and –sqrt3`. 

 


Find α, β are the zeros of polynomial α + β = 6 and αβ = 4 then write the polynomial. 


If the sum of the zeros of the quadratic polynomial kx2 – 3x + 5 is 1, write the value of k.


Find the sum of the zeros and the product of zeros of a quadratic polynomial are `-1/2` and –3 respectively. Write the polynomial.


Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.


If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.


If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then ______.


If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.


A quadratic polynomial, whose zeores are -4 and -5, is ______.


The zeroes of the quadratic polynomial x² + 1750x + 175000 are ______.


If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.


The number of polynomials having zeroes as -2 and 5 is ______.


If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.


The zeroes of the polynomial 3x2 + 11x – 4 are ______.


The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.


The given linear polynomial y = f(x) has


Share
Notifications

Englishрд╣рд┐рдВрджреАрдорд░рд╛рдареА


      Forgot password?
Use app×