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Zeroes of the quadratic polynomial ax2 + bx + c and roots of the quadratic equation ax2 + bx + c = 0 are ——–
- a)Equal to zero
- b)Different
- c)Same
- d)Either same or different
Correct answer is option 'C'. Can you explain this answer?
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Zeroes of the quadratic polynomial ax2+ bx + c and roots of the quadra...
Zeros of the polynomial means the value of variable such that the equation is equal to zero.Roots of the equation means the value of the variable for which LHS=RHS which basically means that the equation is equal to zero. Hence Zeros and roots are one and the same thing.
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Zeroes of the quadratic polynomial ax2+ bx + c and roots of the quadra...
Understanding the Relationship Between Zeroes and Roots
The zeroes of a quadratic polynomial and the roots of its corresponding quadratic equation are intrinsically linked concepts in algebra.
Definition of Zeroes and Roots
- The zeroes of a quadratic polynomial ax² + bx + c are the values of x that make the polynomial equal to zero.
- The roots of the quadratic equation ax² + bx + c = 0 are the solutions to this equation.
Key Connection
- Both terms refer to the same values of x where the polynomial intersects the x-axis. Thus, they are essentially the same mathematical entities expressed in different contexts.
Discriminant Analysis
- The nature of the roots (or zeroes) can be determined using the discriminant (D = b² - 4ac):
- If D > 0: Two distinct real roots (zeroes).
- If D = 0: One real root (zero), indicating the roots are equal.
- If D < 0:="" no="" real="" roots="" (zeroes),="" only="" complex="" />
Conclusion
- The statement that the zeroes of the quadratic polynomial and the roots of the quadratic equation are "same" is correct because they represent the same concept.
- Therefore, option 'C' is the appropriate choice, as both zeroes and roots indicate the values where the polynomial equals zero.
In summary, understanding that the zeroes of a polynomial and the roots of its equation are synonymous is crucial for grasping the fundamentals of quadratic functions.
The zeroes of a quadratic polynomial and the roots of its corresponding quadratic equation are intrinsically linked concepts in algebra.
Definition of Zeroes and Roots
- The zeroes of a quadratic polynomial ax² + bx + c are the values of x that make the polynomial equal to zero.
- The roots of the quadratic equation ax² + bx + c = 0 are the solutions to this equation.
Key Connection
- Both terms refer to the same values of x where the polynomial intersects the x-axis. Thus, they are essentially the same mathematical entities expressed in different contexts.
Discriminant Analysis
- The nature of the roots (or zeroes) can be determined using the discriminant (D = b² - 4ac):
- If D > 0: Two distinct real roots (zeroes).
- If D = 0: One real root (zero), indicating the roots are equal.
- If D < 0:="" no="" real="" roots="" (zeroes),="" only="" complex="" />
Conclusion
- The statement that the zeroes of the quadratic polynomial and the roots of the quadratic equation are "same" is correct because they represent the same concept.
- Therefore, option 'C' is the appropriate choice, as both zeroes and roots indicate the values where the polynomial equals zero.
In summary, understanding that the zeroes of a polynomial and the roots of its equation are synonymous is crucial for grasping the fundamentals of quadratic functions.
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Zeroes of the quadratic polynomial ax2+ bx + c and roots of the quadra...
Same because roots and zeroes of polynomial means same thing
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Zeroes of the quadratic polynomial ax2+ bx + c and roots of the quadratic equation ax2+ bx + c = 0 are ——–a)Equal to zerob)Differentc)Samed)Either same or differentCorrect answer is option 'C'. Can you explain this answer?
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