if a and b zeros of the polynomial x2-2x-15,then form a quadratic polynomial whose zeros are 2a and 2b
Answers
Answer:
So, (x-p)(x-q)=0.
=>x^2-(p+q)x+pq=0
So, the polynomial is x^2-(p+q)x+pq
If given polynomial is ax^2+bx+c. Then let us multiply the polynomial we have derived by a and equated then polynomial coefficients must be same.
Derived polynomial is ax^2-a(p+q)x+apq
So, b=-a(p+q); c=apq.
If required zeroes are kp and kq then, required polynomial is
ax^2–a(kp+kq)+a(kp)(kq)
=ax^2–ka(p+q)+ak^2(k^2)(pq)
We know that b=-a(p+q); c=apq.
Hence, new polynomial is
ax^2+kbx+k^2c
In new polynomial coefficients are multiplied by 1, k and k^2 for Second power, first power and constant terms respectively.
Hence for our polynomial ( x²-2x -15) and new required zeroes (double), the polynomial is
x² -4x -60.
For this particular polynomial let us take the following equation
x^2–2x-15=0
=>x^2–5x+3x-15=0
=>x(x–5)+3(x-5)=0
=>(x–5)(x+3)=0
Hence x=5 or x=-3 are solutions of equation. Hence, ther are zeros of polynomial.
New zeroes are 10 and -6.
Hence, new equation is (x-10)(x+6)=0.
So, new equation is x^2–4x-60=0.
So, required polynomial is x^2–4x-60
Ans.: x^2–4x-60
Answer:
x² - 4x - 60
Step-by-step explanation:
See the Attachment
